Colloquia, Lectures & Seminars
Colloquia and Seminars (Fall 2024 / Spring 2025)
TACO Seminar:
http://gauss.math.luc.edu/algcomb/
Data Science Seminar:
https://www.luc.edu/datascience/events/datascienceseminar/
Analysis Seminar:
https://fermat.math.luc.edu/analysis_seminar/
When: October 17, 2024
Location: TBD
Time: 4:00-5:00pm
Speakers: Dr. Sven Leyffer, https://www.anl.gov/profile/sven-leyffer
Topic: Topological Design Problems and Integer Optimization
Description: Topological design problems arise in many important engineering and scientific applications, such additive manufacturing and the design of cloaking devices. We formulate these problems as massive mixed-integer PDE-constrained optimization (MIPDECO) problems. We show that despite their seemingly hopeless complexity, MIPDECOs can be solved efficiently (at a cost comparable to a single continuous PDE-constrained optimization solve). We discuss two classes of methods: rounding techniques that are shown to be asymptotically optimal, and trust-region techniques that converge under mesh refinement. We illustrate these solution techniques with examples from topology optimization.
When: September 26, 2024
Location: IES 124
Time: 4:00-5:00pm
Speakers: Sergio Alejandro Fernandez de Soto Guerrero (Graz University of Technology)
Topic: Undergraduate research
Description:
Abstract: Cumulative imaging dose to healthy tissue outside the high-dose radiation field during image-guided radiation therapy (IGRT) may increase the risk of developing complications. As such, there is a clinical need to reduce the imaging dose associated with IGRT without compromising image quality. The purpose of this study is to examine the feasibility of training a neural network to produce cone-beam computed tomography (CBCT) scans with image quality on par with current clinical usage while reducing the cumulative imaging dose to patients.
Maggie Gonzalez: Ocean robots reveal the importance of Antarctic Winter Water to the global carbon cycle.
Abstract: Antarctic Winter Water, sections of cold water trapped between relatively warm sections of water above and below it, is found across the Southern Ocean. Using data collected from floats across the Southern Ocean, we identified and characterized Winter Water and its relationship to carbon subduction, the absorption of carbon dioxide from the atmosphere into the ocean. Our findings reveal the importance of Winter Water to the global carbon cycle, allowing for improved accuracy in our understanding of the processes that contribute to climate change.
Melissa Beerbower: Lucky Sets of Fubini Rankings
Abstract: One subset of parking functions is the set of Fubini rankings, which encode the outcomes of n competitors in a race where ties are allowed. The number of lucky cars in a Fubini ranking is equivalent to the number of distinct ranks, k. We enumerate Fubini rankings and some subsets recursively through fixed sets of lucky competitors. Our enumerations explain twin coefficients for minimum powers in the lucky polynomial of l-interval Fubini rankings.
When: September 19, 2024
Location: IES 111
Time: 4:00-5:00pm
Speakers: Sergio Alejandro Fernandez de Soto Guerrero (Graz University of Technology)
Topic: MathMagic: A positroidal action over a deck of cards
Description: Positroids are a subclass of matroids born in the study of the non-negative Grassmanian by Postnikov in 2006. Since then, there have been a plethora of combinatorial objects indexing positroids, two of these being the families of decorated and bicolored permutations, which are generalizations of classical permutations. These two families can be used to study properties of positroids, and as a byproduct we end up with useful ways to describe a group action on a deck of cards. In this context, we give a definition of invariants under this group action allowing us, as an application, to develop new magic tricks with unusual ways of shuffling cards.
When: September 17, 2024
Location: IES 110
Time: 4:00-5:00pm
Speakers: Andrew Ducharme (University of Oregon)
Topic: Fourier analysis of highly oscillatory functions e^{i*t(x)}
Description: The Fourier transform is a fundamental and ubiquitous mathematical tool for writing an arbitrary function in terms of an infinite series of sines and cosines. In optics, Fourier transforms describe how light is focused by a lens. Rigorously, light traveling through an object t(x) thick is focused into bright spots whose intensities depend on the Fourier transform of e^{i*t(x)}=cos(t(x))+i sin(t(x)). These second ¿highly oscillating¿ functions are difficult to analyze, so the physics literature contains very few closed-form results regarding this class of functions. An exciting exception is known procedures for producing functions t(x) which optimize their output into exactly two, or three, or n equal beams.
Symmetric 2D outputs, like four points which are the vertices of a square, are optimized by asymmetric functions t(x,y). It is often forgotten that we do not know if the symmetric 1D functions called ¿optimal¿ are truly the best possible. I will discuss our work searching for ¿loophole¿ beamsplitters, asymmetric functions which outperform the best-known symmetric functions for optimizing intensity into n points. I will additionally show five novel highly oscillating functions we have found closed-form results for.
When: September 12, 2024
Location: IES 124
Time: 4:00-5:00pm
Speakers: Sarah Riaz, Amanda Newton, and Anurathi Madasi
Topic: Undergraduate research
Description: We will have three talks on exciting research done by our undergraduate students over the past year.
Sarah Riaz: Using Permutations to Investigating the Waffle Puzzle.
The waffle puzzle is a Wordle-type puzzle game in which you are given all the letters to make 6 words on a 5x5 board and must rearrange them by swapping only two letters at a time. This research shows some methods for getting to the solution in the least amount of swaps once we have the solution state and the number of possible types of waffles and solutions to them.
Amanda Newton: Spins of Intermediate Mass Black Holes in Galactic Nuclei From Black Hole-Star Collisions.
In galactic nuclei, black holes (BHs) collide often with stars due to the high density and velocity dispersion in this environment. In these collisions, BHs accrete mass from the stars. Because of the frequent collisions, BHs may accrete large amounts of mass, and grow into larger BHs than when formed through star death alone. We study how BH spin changes in these collisions through a simulation in order to understand the relationship between spin change and mass change in these BH-star collisions.
Anurathi Madasi: Optical and Near-Infrared Searches for Gravitational Waves: Exploring Efficiencies
The Laser Interferometer Gravitational-Wave Observatory(LIGO) is able to detect ripples in
spacetime caused by a binary black hole or binary neutron star mergers known as gravitational
waves(GW). Some of these GW events can have an electromagnetic(EM) counterpart, which can be seen optically using a telescope. This is known as multi-messenger astronomy, and having multiple sources of the same event provides insight into what the object is, where it from, etc. In our project, we aimed to test the efficiency of the Zwicky Transient Facility(ZTF) at detecting kilonovae. We populate a skymap with kilonovae, and test how many kilonovae ZTF can detect compared to how many we simulated. We updated our code from simsurvey, which is no longer being maintained, to skysurvey.
A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Those are known as generalized Fibonacci polynomials GFP. Some known examples are: Fibobacci Polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials, Vieta and Vieta-Lucas polynomials.
It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the strong divisibility property. However, this property does not hold for every second order recursive sequence. We give a characterization of GFPs that satisfy the strong divisibility property. We also give formulas to evaluate the gcd of GFPs that do not satisfy the strong divisibility property.
In the end of the talk we talk about the irreducibility of GFP. Joint work with M. Diaz-Noguera, R. Higuita, M. Romero-Rojas, R. Ramirez, and J.C. Saunders.
Colloquia and Seminars (Fall 2023 / Spring 2024)
TACO Seminar:
http://gauss.math.luc.edu/algcomb/
Data Science Seminar:
https://www.luc.edu/datascience/events/datascienceseminar/
Analysis Seminar:
https://fermat.math.luc.edu/analysis_seminar/
When: April 18, 2024
Location: IES 110
Time: 4:00-5:00pm
Speaker: Rigoberto Florez
Topic: The strong divisibility property and the resultant of generalized Fibonacci polynomials
Description: A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Those are known as generalized Fibonacci polynomials GFP. Some known examples are: Fibobacci Polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials, Vieta and Vieta-Lucas polynomials.
It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the strong divisibility property. However, this property does not hold for every second order recursive sequence. We give a characterization of GFPs that satisfy the strong divisibility property. We also give formulas to evaluate the gcd of GFPs that do not satisfy the strong divisibility property.
In the end of the talk we talk about the irreducibility of GFP. Joint work with M. Diaz-Noguera, R. Higuita, M. Romero-Rojas, R. Ramirez, and J.C. Saunders.
Bio: Dr. Florez is an Associate Professor with a Ph.D. in Mathematics from Binghamton University (SUNY). His research is in combinatorics, especially graphs and algebraically representable matroids. He is also interested in elementary number theory and enumerative combinatorics. Rigo likes working research projects with undergraduate and graduate students. His students have presented their research in local and national conferences and they have won awards doing the same. He is one of the founders of Carolina Math Seminar.
When: April 11, 2024
Location: IES 110
Time: 4:00-5:00pm
Speaker: Frank Baginski
Topic: The Shape of a High Altitude Balloon
Description: Much of the research in the upper stratosphere (35 km and above) is conducted using large scientific balloons. These balloons are not to be confused with their tiny cousins, weather balloons. The payload of a large scientific balloon can be several thousand pounds. The largest balloon is roughly 130 meters tall with a diameter of 160 meter. A typical balloon is constructed from 40 micron polyethylene (i.e., sandwich bag thickness). In the analysis of these unique structures, a number of interesting mathematical questions arise. What is the shape of the balloon at float altitude ? How is the shape designed? How is the balloon system launched? Will it deploy into the desired shape? The workhorse for NASA's Balloon Program is the (onion shaped) zero-pressure balloon. A newcomer is the (pumpkin shaped) super-pressure balloon. The answers to these and related questions lead to some interesting mathematical problems that will be discussed during the talk.
Bio: Frank Baginski received his Ph.D in Applied Mathematics from the University of Massachusetts, Amherst in 1985 and is Professor of Mathematics at George Washington University. He has collaborated with mathematicians, engineers, and physicists on modeling high altitude large scientific balloons, aerodynamic decelerators, and large-aperture reflectors.
When: February 29, 2024
Location: IES 110
Time: 4:00-5:00pm
Speaker: Claudia Solís-Lemus
Topic: Inferring biological networks
Description: Networks are graphical structures that appear in a variety of biological applications from phylogenetic networks to study evolution to interaction networks to study microbial communities in soil and plants. I will describe the novel statistical advances (and challenges) to estimate 1) phylogenetic networks from genome-wide data, and 2) microbial networks from abundance data. I will conclude with some examples of how deep learning models can be applicable to infer these types of networks.
Bio: I am an assistant professor at the Wisconsin Institute for Discovery and the Department of Plant Pathology at the University of Wisconsin-Madison. Originally from Mexico City, I did my Undergraduate degrees in Actuarial Sciences and Applied Mathematics at ITAM. Then, I did a MA in Mathematics and a PhD in Statistics at the University of Wisconsin-Madison.
When: January 29, 2024
Location: Dumbach 227
Time: 4:15-5:15pm
Speaker: Dr. Emma Zajdela
Topic: Catalyzing collaborations: Modeling scientific team formation for global impacts.
Description: I will talk about my research on modeling scientific collaboration at in-person and virtual conferences, and also include some background on my activities in science diplomacy which started while I was at Loyola and inspired this work.
Bio: Emma Zajdela is a Loyola Alum with a 2016 BS from our department. Since then she completed an MS in Applied Math from UIC and a Ph.D. in Engineering Sciences and Applied Math from Northwestern. She is now a Postdoctoral Fellow at Princeton. Her research focuses on developing mathematical models to understand and predict complex social phenomena. She has used this to study topics ranging from poker to autonomous vehicles to scientific collaboration to fashion trends.
When: December 7, 2023
Location: IES 110
Time: 4:00-5:00pm
Speaker: Elizabeth Gross, Associate Professor, Department of Mathematics, University of Hawai`i at M¿noa
Title: The Algebra and Geometry of Evolutionary Biology
Abstract: One of the main goals of evolutionary biology is to understand the evolutionary history of a set of species. These histories can aid in conservation efforts and are represented by directed graphs where the leaves represent living species and the interior nodes represent extinct species. While it is common to assume evolutionary histories are trees, when events such as hybridization are present, networks are more realistic. However, allowing for networks complicates the process of inference, and ways to overcome this complication are needed. One recent approach to phylogenetic network inference is rooted in algebra and geometry. In this talk, we discuss the role algebra and geometry has played in the statistical problems related to network inference and show how these tools combined with statistical learning can aid in network reconstruction.
When: November 16, 2023
Location: IES 124
Time: 4:00-5:00pm
Speaker: Albert S. Berahas (University of Michigan)
Title: Next Generation Algorithms for Stochastic Optimization with Constraints
Abstract: Stochastic gradient and related methods for solving stochastic optimization problems have been studied extensively in recent years. It has been shown that such algorithms and much of their convergence and complexity guarantees extend in straightforward ways when one considers problems involving simple constraints, such as when one can perform projections onto the feasible region of the problem. However, settings with general nonlinear constraints have received less attention, and many of the approaches that have been proposed for solving such problems resort to using penalty or (augmented) Lagrangian methods, which are often not the most effective strategies. In this work, we propose and analyze stochastic optimization algorithms for deterministically constrained problems based on the sequential quadratic optimization (commonly known as SQP) methodology. We discuss the rationale behind our proposed techniques, convergence in expectation and complexity guarantees for our algorithms, and present numerical experiments that we have performed. This is joint work with Raghu Bollapragada, Frank E. Curtis, Michael O'Neill, Daniel P. Robinson, Jiahao Shi and Baoyu Zhou.
About the speaker: Albert S. Berahas is an Assistant Professor in the Industrial and Operations Engineering department at the University of Michigan. Before joining the University of Michigan, he was a Postdoctoral Research Fellow in the Industrial and Systems Engineering department at Lehigh University working with Professors Katya Scheinberg, Frank Curtis and Martin Takáč. Prior to that appointment, he was a Postdoctoral Research Fellow in the Industrial Engineering and Management Sciences department at Northwestern University working with ProfessorJorge Nocedal. Berahas completed his PhD studies in the Engineering Sciences and Applied Mathematics (ESAM) department at Northwestern University in 2018, advised by Professor Jorge Nocedal. He received his undergraduate degree in Operations Research and Industrial Engineering (ORIE) from Cornell University in 2009, and in 2012 obtained an MS degree in Applied Mathematics from Northwestern University. Berahas’ research broadly focuses on designing, developing and analyzing algorithms for solving large scale nonlinear optimization problems. Specifically, he is interested in and has explored several sub-fields of nonlinear optimization such as: (i) general nonlinear optimization algorithms, (ii) optimization algorithms for machine learning, (iii) constrained optimization, (iv) stochastic optimization, (v) derivative-free optimization, and (vi) distributed optimization. Berahas is served as the vice-chair of the Nonlinear Optimization cluster for the INFORMS Optimization Society (2020-2022), the chair of the Nonlinear Optimization cluster for the INFORMS Optimization Society Conference (2021-2022), and the co-chair of the Nonlinear Optimization cluster for the ICCOPT 2022 conference (2021-2022). Berahas is the president of the INFORMS Junior Faculty Interest Group (JFIG).
When: November 7, 2023
Location: IES 111
Time: 4:00-5:00pm
Speakers: Cecily Bartsch, Cole Fleming, and Kathryn Cantrell.
Details: We will have three talks on exciting research done by our undergraduate students over the past year.
When: October 12, 2023
Location: IES 111
Time: 4:00-5:00pm
Speakers: Isabel Rentería, Amanda Newton, and Anurathi Madasi
Details: We will have three talks on exciting research done by our undergraduate students over the past year.
Colloquia and Seminars (Fall 2022 / Spring 2023)
TACO Seminar:
http://gauss.math.luc.edu/algcomb/
Data Science Seminar:
https://www.luc.edu/datascience/events/datascienceseminar/
When: Thursday, April 20, 2023
Location: IES 110
Lecture: 4:00-5:00pm
Speaker: Dr. Rebecca Willett (University of Chicago)
Title: Machine learning and data assimilation in the natural sciences and engineering
Abstract: The potential for machine learning to revolutionize scientific and engineering research is immense, but its transformative power cannot be fully harnessed through the use of off-the-shelf tools alone. To unlock this potential, novel methods are needed to integrate physical models and constraints into learning systems, accelerate simulations, and quantify model prediction uncertainty. In this presentation, we will explore the opportunities and emerging tools available to address these challenges in the context of inverse problems, data assimilation, and reduced order modeling. By leveraging ideas from statistics, optimization, scientific computing, and signal processing, we can develop new and more effective machine learning methods that improve predictive accuracy and computational efficiency in the natural sciences.
About the speaker: Dr. Willett is a Professor of Statistics and Computer Science & Director of AI at the Data Science Institute, with a courtesy appointment at the Toyota Technological Institute at Chicago. She is also the faculty lead of AI+Science Postdoctoral Fellow program. Prof. Willett’s work in machine learning and signal processing reflects broad and interdisciplinary expertise and perspectives. She is known internationally for her contributions to the mathematical foundations of machine learning, large-scale data science, and computational imaging. In addition to her technical contributions, Prof. Willett is a strong advocate for diversity in STEM and AI and has organized multiple events to support women in middle school, as undergraduate and graduate students, and as faculty members.
https://willett.psd.uchicago.edu
When: Thursday, April 13, 2023
Location: IES 110
Lecture: 4:00-5:00pm
Speaker: Rrita Zejnullahi
Title: Fund allocation for poverty alleviation
Abstract: In this talk, we consider the problem of how to optimally allocate a finite amount of resources across different locations/populations. While this decision task has wide application (e.g., allocation of health care funds to different populations, allocation of vaccines to different locations), we focus on the problem of reducing national poverty via sub-national cash transfers. Though an optimal strategy has long been identified in this situation, understanding the impact of estimation uncertainty of the needs of different groups/locations on the vector of allocations, and incorporating these into the optimal targeting procedure has not yet been formally addressed. Through simulations, we illustrate the consequences of ignoring estimation uncertainty on the vector of allocations. We then identify a strategy that formally accounts for this error. This presentation will cover work in progress.
About the speaker: Rrita Zejnullahi is a Postdoctoral Researcher in the Department of Statistics at the University of Washington, working on the development of a decision-making framework for policy decisions based on predictions from statistical models. Previously, she obtained a PhD in Statistics from Northwestern University, where she focused on small-sample methods for meta-analysis, with applications to education, medicine and the social sciences.
When: Monday, March 20, 2023
Location: IES 124
Lecture: 4:00-5:00pm
Speaker: Sarah Bockting-Conrad
Title: A Journey Toward Tridiagonal Pairs
Abstract: Tridiagonal pairs are fascinating objects with connections to many other areas of mathematics and physics. While their definition involves only linear algebra, the study of tridiagonal pairs has its origins in algebraic graph theory. In this talk, we start with some basic notions in graph theory and work our way toward showing how tridiagonal pairs arise naturally from the study of a certain special family of graphs. With this motivation in mind, we define tridiagonal pairs, discuss some of their properties, and describe their importance to algebraic graph theory.
About the speaker: Dr. Bockting-Conrad earned her PhD in Mathematics from the University of Wisconsin-Madison in 2014. She then served as a Visiting Assistant Professor at Oberlin College for one year before joining the faculty at DePaul University in 2015.
When: Thursday, December 1, 2022
Location: IES 110
Lecture: 4:00-5:00pm
Speaker: Dr. Pamela E. Harris (University of Wisconsin at Milwaukee)
Title: Multiplex juggling sequences and Kostant's partition function
Abstract: Multiplex juggling sequences are generalizations of juggling sequences (describing throws of balls at discrete heights) that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. Kostant¿s partition function is a vector function that counts the number of ways one can express a vector as a nonnegative integer linear combination of a fixed set of vectors. What do these two families of combinatorial objects have in common? Attend this talk to find out!
About the speaker: Dr. Harris is an Associate Professor in the Department of Mathematical Sciences at the University of Wisconsin at Milwaukee. She also cohosts the podcast Mathematically Uncensored and is the President and co-founder of Lathisms: Latinxs and Hispanics in the Mathematical Sciences. Her research interests are in algebra and combinatorics, particularly as these subjects relate to the representation theory of Lie algebras.
When: Thursday, November 17, 2022
Location: IES 110
Lecture: 4:00 – 5:00 p.m.
Speaker: Mena Whalen - Loyola University Chicago
Title: History of Statistics: Introductory Statistics and the People Behind It
Abstract: Learn more about how topics in introductory statistics courses came to be and the men behind the methods. This will be a lecture and discussion walking through the early 1900's following the development of Pearson, Fisher, and Neyman as researchers discovering revolutionary methods like design of experiments, chi-squared goodness of fit test, and likelihood ratio test. Come understand the context of these researchers' interactions with each other and the lasting impact they had on the field.
About the speaker: Dr. Whalen is an assistant professor of statistics in the department of mathematics and statistics at Loyola University Chicago. Her research interest includes time series analysis with an emphasis in change point analysis, spatial analysis, data science with data visualization, and network models. Special topic interest includes health policy, law and policy change, and criminology. She is an ambassador and co-organizer of the Women in Data Science (WiDS) conference for Chicago.
When: Thursday, October 20, 2022
Location: Mundelein 609
Lecture: 3:00 – 4:00 p.m.
Speaker: Michelle Yuanying Guan - DePaul University
Title: Network Models in Finance and Insurance
Abstract: The financial systems can be perceived as a complex interacting system and networks of financial institutions exhibit complex structures. In this presentation, we will show how different network structures have an impact on the spread of financial risk among financial institutions. We will also investigate how these network structures can be applied to the study of cyber risk in the insurance field.
About the speaker: Dr. Guan earned her PhD in Financial Mathematics from Florida State University in 2011. Prior to joining the faculty at DePaul University in 2020, Dr. Guan served as an Associate Professor and the Actuarial Science Advisor in the Department of Mathematics and Actuarial Science at Indiana University Northwest.
Dr. Guan is an Associate of the Society of Actuaries (ASA). Her research interests are in financial mathematics and actuarial science, focusing on heterogeneous agent models in asset pricing and systemic risk in financial systems.
When: Wednesday, September 28, 2022
Location: Cuneo 217
Lecture: 3:50 – 4:40 p.m.
Speaker: Rafael González D'León - Loyola University Chicago (Mathematics and Statistics Department)
Title: Flow polytopes as a unifying framework for some familiar combinatorial objects
Abstract: Flow polytopes are a family of beautiful geometric objects which have connections to many areas in mathematics including optimization and representation theory. Computing their volumes and enumerating lattice points of some particular flow polytopes turn out to be combinatorially interesting problems that involve beautiful enumeration formulas and many familiar combinatorial objects. Baldoni and Vergne found a series of formulas for both of these purposes, which they call Lidskii formulas, that are combinatorially powerful and pleasant. A later proof of the Lidskii formulas has been achieved by Mészáros and Morales, following the ideas of Postnikov and Stanley, using polytopal subdivisions. For a smaller class of flow polytopes, these subdivisions are triangulations that coincide with a family of framed triangulations defined by Danilov, Karzanov, and Koshevoy. These triangulations have interesting hidden combinatorial structure. We will give an introduction to flow polytopes and these formulas, including some recent applications, and a series of open problems and conjectures which we are currently working on.
About the speaker: Rafael González D'León is a mathematics professor at LUC. His research interests include enumerative, geometric, topological and algebraic combinatorics, algebraic objects supported on combinatorial structures, and the mathematics of RNA folding.
When: Wednesday, September 21, 2022
Location: BVM Hall, Room 1102
Lecture: 3:50 – 4:40 p.m.
Speaker: Emily Peters - Loyola University Chicago (Mathematics and Statistics Department)
Title: The classification of Frobenius algebras
Abstract: Frobenius algebras are both (1) a reasonably straightforward type of algebra, which in addition to a unit and multiplication also have a co-unit and co-multiplication, and (2) fundamental to the classification of 2D topological quantum fields theories (TQFTs), making them part of "baby model for quantum gravity" (according to Joaquim Kock). In this talk I will define the key players and go into detail about the classification of Frobenius algebras.
About the speaker: Professor Peters is a mathematics professor at LUC. Her research focuses on subfactors, planar algebras, and knot theory.
Tea and Colloquia (Fall 2021 / Spring 2022)
When: Thursday, March 17, 2022
Location: IES, Room 123
Lecture: 4:00 – 5:00 p.m.
Speaker: James M. Cheverud - Loyola University Chicago (Biology Department)
Title: Quantitative Genetics
Abstract: I'll talk about my field, quantitative genetics, and how evolutionary theory became mathematical. I'll also describe some challenges in the quantitative analysis revolving around negative semi-definite variance/covariance matrices.
About the speaker: Professor Cheverud is the Chair of the Department of Biology at LUC. His research focuses on evolutionary genetics, morphology, the genetics of complex traits and diseases in model organisms, and primate and mammalian evolution.
When: Thursday, December 2, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Ian Tobasco - University of Illinois at Chicago
Title: Effective Geometries in Elasticity: Wrinkles and Planar Kirigami
Abstract: What do wrinkles and shape-morphing sheets have in common? The answer is fine scale buckling — a patterned response driven by mechanical instabilities enabling macroscopic shape change beyond bulk elasticity. This talk will highlight two recent developments in the mathematics of materials leading to new predictions for (i) the zoo of wrinkle patterns that form when a shell is incompatibly confined, and (ii) the aggregate deformations of kirigami sheets made by removing a lattice of holes. Behind both advances is the concept of an “effective geometrical description” in which the underlying patterns are “averaged out”. Systematic energy minimization leads to a limiting description in which the effective geometry can be found, sometimes even by hand. Our story reminds of the classical homogenization of composites, but with fine scale buckling patterns in place of a rapidly oscillating material law. Finding effective geometries is a key step towards a mechanical theory of shape change.
About the speaker: Ian Tobasco is an Assistant Professor at the University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science. He holds a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences at New York University, and a B.S.E. in Aerospace Engineering from the University of Michigan. Tobasco works at the interface of mathematics, physics, and engineering, where advances in analysis can lead to scientific breakthroughs in the lab and vice versa. Besides elasticity, Tobasco’s current interests include the search for optimal transport mechanisms in fluid dynamics, and their comparison with naturally turbulent flows.
When: Thursday, November 18, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Jacob Michael Schauer
Title: The Statistics of Replication: Considerations and Pitfalls
Abstract: Recent research has questioned the replicability of scientific findings in various fields, including medicine, economics, and psychology. This research has also revealed that there is no standard analysis methods for replication. As a result, it is not clear how we should be designing and analyzing replication studies. This talk describes statistical considerations for studying replication, and examines their implications. It identifies some surprising statistical strengths and limitations of previous research, including the use of statistical methods with surprisingly high error rates. It then argues that such issues can be avoided in future efforts by taking into account key statistical considerations in the planning and analysis of replication studies.
About the speaker: Dr. Schauer is an Assistant Professor of Preventive Medicine at Northwestern University's Feinberg School of Medicine. His research interests include methods for studying replication, modern advances in meta-analysis, approaches to missing data, and data privacy.
When: Thursday, November 4, 2021
Location: Online (Zoom: HTTPS://LUC.ZOOM.US/J/81081283725 )
Lecture: 4:30 – 5:30 p.m.
Speaker: Hakan Demirtas (University of Illinois at Chicago)
Title: Hybrid data generation
Abstract: This talk formulates a plan for implementing a unified, general-purpose mixed data generation framework that includes nearly all major types of variables (i.e., binary, ordinal, count, and continuous) when the marginal distributions and a feasible association structure in the form of Pearson or Spearman correlations are specified for simulation purposes via a mathematically unsophisticated but effective sorting procedure.
Most relevant papers:
Demirtas, H. & Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. American Statistician, Volume 65, Issue 2, 104-109.
Demirtas, H. (2019). Inducing any feasible level of correlation to bivariate data with any marginals. American Statistician, Volume 73, Issue 3, 273-277.
About the speaker: Dr. Demirtas is an Associate Professor of Biostatistics at the Division of Epidemiology and Biostatistics in University of Illinois at Chicago. His research interests include missing data, statistical computing, multiple imputation, stochastic simulation, and random number generation
When: Thursday, October 28, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Sameer Deshpande (University of Wisconsin)
Title: Simultaneous variable and covariance selection with the multivariate spike-and-slab LASSO
Abstract: We consider multivariate linear regression models in which the goal is to predict q possibly correlated responses using a common set of p predictors. In these problems, interest lies not only in determining whether or not a particular predictor has an effect on each response but also in understanding the residual dependence between the outcomes. We propose a Bayesian procedure for such determination using continuous spike-and-slab priors. Rather than relying on a stochastic search through the high-dimensional parameter space, we develop an Expectation-Maximization algorithm targeting modal estimates of the matrix of regression coefficients and residual precision matrix. A key feature of our method is the model of our uncertainty about which parameters are negligible. Essentially, this model enables us to shrink parameters to zero in an automatic and data-adaptive fashion. Our method is seen to substantially outperform regularization competitors that employ fixed penalties on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several late-life cognitive psychological, and socioeconomic outcomes.
About the speaker: Dr. Deshpande is an Assistant Professor in Statistics Department at the University of Wisconsin - Madison. His research interests include Bayesian hierarchical modeling, treed regression, model selection, and causal inference with applications in public health and sports.
When: Thursday, October 21, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Tung Nguyen
Title: Acyclic digraphs and an algebraic construction of cospectral digraphs
Abstract: Graph theory plays a fundamental role in science and real-life applications. It is the architect for the Internet, the world wide web, biological networks, utility infrastructures, social networks, and much more.
One of the most important and interesting invariances of a graph is its spectrum which is defined as the set of eigenvalues of its adjacency matrix. The spectrum of a graph is crucial for many applications such as Google search algorithms, non-linear dynamics, controller design, data analysis, etc.
Two graphs are called isospectral if they share the same spectrum. In this talk, I will explain a new algebraic approach to the construction of isospectral graphs. This is a simple construction that has strong potential to attack some problems in the non-linear dynamics of a complex network of coupling oscillators. This is based on the joint work with Anna Krokhine, Chun Hei Lam, Ton Meesena, William Jones, John Merzel, Jan Minac, Lyle Muller through the 2021 Fields Undergraduate Summer Research Program.
Time permitting, I will briefly discuss my recent joint work and further projects with Sunil Chebolu, Jan Minac, Lyle Muller, and Federico Pasini on some exciting investigations into the spectrum of certain graphs with inspirations from representation theory.
About the speaker: Dr. Nguyen obtained his Ph.D. in 2020 from the University of Chicago with a specialty in algebraic number theory. His recent research interest includes number theory, spectral graph theory, representation theory, dynamical systems, and computational neuroscience.
When: Thursday, October 14, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Mena Whalen (Loyola University Chicago)
Title: Clustering Panels of Nonlinear Time Series Examined Though Chicago Crime During COVID-19
Abstract: When do we think that a time series will change versus when the actual change in behavior occurs is a question many researchers and policy analyst pose. Advances in change point analysis can yield a more precise estimation of a change point, where in time is a time series is changing, but how do we examine and group multiple locations together based on their change points? I propose a methodology that clusters panels of nonlinear time series with change points and point anomalies while accounting for spatial characteristics. This approach groups time series together to identify latent structures that can help researchers understand when and which areas are changing together. This methodology is applied to Chicago neighborhood crime data during the COVID-19 pandemic.
About the speaker: Dr. Whalen is an assistant professor of statistics in the department of mathematics and statistics at Loyola University Chicago. Her research interest includes time series analysis with an emphasis in change point analysis, spatial analysis, data science with data visualization, and network models. Special topic interest includes health policy, law and policy change, and criminology. She is an ambassador and co-organizer of the Women in Data Science (WiDS) conference for Chicago.
When: Thursday, September 30, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Gregory Matthews (Loyola University Chicago)
Title: Shape-Based Classification of Partially Observed Curves with Applications to Anthropology
Abstract: We consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonparametric multiple imputation procedure; (iii) development of nearest neighbor classifiers compatible with the completion techniques. Our contributions are founded on exploiting the geometric notion of shape of a curve, defined as those aspects of a curve that remain unchanged under translations, rotations and reparameterizations. Explicit incorporation of shape information into the computational methods plays the dual role of limiting the set of all possible completions of a curve to those with similar shape while simultaneously enabling more efficient use of training data in the classifier through shape-informed neighborhoods. Our methods are then used for taxonomic classification of partially observed curves arising from images of fossilized extant Bovidae teeth, obtained from a novel anthropological application concerning paleoenvironmental reconstruction.
About the speaker: Dr. Matthews is the Director for Data Science at our Mathematics and Statistics Department. His interests include statistical disclosure control, missing data methods, statistical genetics, and statistics in sports.
When: Thursday, September 23, 2021
Location: Cuneo Hall, Room 311
Lecture: 4:30 – 5:30 p.m.
Speaker: Rafal Goebel (Loyola University Chicago)
Title: The consensus and rendezvous problems
Abstract: The consensus problem for a multi-agent system is about whether the agents (say, autonomous robots or individuals in a social network) can exchange information to reach a common opinion. A special case, known as the rendezvous problem, is about the agents asymptotically arriving at the same location. The challenges lie in the agents only being able to communicate their current opinion/location to their neighbors; in the communication structure changing over time; in constraints on the opinion/location of each agent; etc. The role of mathematics in this is, among other things, to prove that the given information structure and the chosen opinion adjustment/location control strategy works. Focusing on the rendezvous problem, the talk will show how elements of differential equations, linear algebra, graph theory, optimization, convex analysis, and switching dynamical system theory are involved in establishing convergence of the agents to the same location. The talk is based on joint work with Ricardo Sanfelice. 200-level calculus, differential equations, and linear algebra background should suffice for most of the talk.
About the speaker: Professor Goebel joined the Department of Mathematics and Statistics at Loyola University Chicago in 2008. His interests include convex, nonsmooth, and set-valued analysis; control theory, including optimal control; hybrid dynamical systems; and optimization.
Tea and Colloquia (Spring 2021)
When: Friday, April 16, 2021
Lecture: 3:00 – 4:00 p.m.
Speaker: Liubomir Chiriac (Portland State University)
Title: On the number of roots of polynomials modulo primes
Abstract: Given a polynomial with integer coefficients, we consider the number of solutions it has modulo prime numbers p. A classical problem in number theory is to study how this quantity varies with p. We will discuss several explicit examples where it is possible to give a simple rule that determines the number of linear factors in terms of seemingly unrelated objects. In the process, we will touch upon some of the very first instances of the Langlands Reciprocity Conjecture. This talk will be appropriate for undergraduate and graduate students, as well as faculty in all areas of mathematics.
Zoom link: https://luc.zoom.us/j/89406733575
Tea and Colloquia (Fall 2020)
When: Thursday, October 29, 2020 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Dr. Matthews, Professor of Statistics at Loyola University Chicago
Title: Bang the Can Slowly: An Investigation into the 2017 Houston Astros
Abstract: This manuscript is a statistical investigation into the 2017 Major League Baseball scandal involving the Houston Astros, the World Series championship winner that same year. The Astros were alleged to have stolen their opponents' pitching signs in order to provide their batters with a potentially unfair advantage. This work finds compelling evidence that the Astros on-field performance was significantly affected by their sign-stealing ploy and quantifies the effects. The three main findings in the manuscript are: 1) the Astros' odds of swinging at a pitch were reduced by approximately 27% (OR: 0.725, 95% CI: (0.618, 0.850)) when the sign was stolen, 2) when an Astros player swung, the odds of making contact with the ball increased roughly 80% (OR: 1.805, 95% CI: (1.342, 2.675)) on non-fastball pitches, and 3) when the Astros made contact with a ball on a pitch in which the sign was known, the ball's exit velocity (launch speed) increased on average by 2.386 (95% CI: (0.334, 4.451)) miles per hour.
Regular Events
For more information, follow the links to the seminar pages.
- Algebra and Combinatorics Seminar
- Analysis Seminar
- Teaching Seminar
- Undergraduate Colloquium in the Mathematical Sciences
- Statistics Seminar (see calendar)
Past Events
When: Thursday, October 22 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Wai Tong Fan, Professor of Mathematics at Indiana University Bloomington
Title: Identification and estimation for Markov processes on phylogenetic trees
Abstract: In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and branchings indicate past speciation events. Phylogenies are commonly estimated from DNA sequences collected from the species of interest. In order to obtain accurate estimates in phylogenetic analyses, it is standard practice to employ statistical approaches based on stochastic models of sequence evolution on a tree. For tractability, such models necessarily make simplifying assumptions about the evolutionary mechanisms involved. In particular, commonly omitted are insertions and deletions of nucleotides -- also known as indels. Properly accounting for indels in statistical phylogenetic analyses remains a major challenge in computational evolutionary biology. In this expository talk, we consider two fundamental questions in evolutionary biology and information theory. Namely, reconstructing the ancestral sequence and the phylogeny in a model of sequence evolution incorporating nucleotide substitutions, insertions and deletions. We shall consider the case of dense phylogenies of bounded height, which we refer to as the taxon-rich setting, where statistical consistency is achievable. We give the first polynomial-time ancestral reconstruction algorithm with provable guarantees.
When: Thursday, October 15 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Gabriel Ngwe
Title: On Computable Numbers
Abstract: A real number is said to be computable if, given a natural number n, there is a procedure that can calculate the decimal expansion accurate to n decimal places. In this talk we give an overview of computable numbers, provide examples of numbers that are not computable, and give some surprising results concerning these numbers.
When: Thursday, September 24 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Nathan Lopez
Title: A random triangle takes up 15% of its inscribing circle
Abstract: I’ll explore some applications of calculus to geometry, specifically using optimization and the average vale of a function. The talk is aimed at undergraduates who have taken or are currently taking calculus 2 or above.
When: Thursday, September 17 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Dr. Seguin, Professor of Mathematics at Loyola University Chicago
Title: Generating a Developable Surface from a Space Curve
Abstract: A developable surface is one in which near each point, there is a patch of the surface that can be flattened without distorting it. Such surfaces include cones and cylinders and appear ubiquitously in engineering applications and architectural design. Given a space curve, there are two natural ways to generate a developable surface from it. These are the so called tangent developable and rectifying developable surfaces. In my talk I’ll discuss how these correspond to endpoints of a spectrum of developable surfaces that can be constructed from a space curve. The talk will contains numerous figures to illustrate the different types of developable surfaces I’ll be discussing.
When: Thursday, September 10 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Dr. Tingley, Professor of Mathematics and Department Chair at Loyola University Chicago
Title: Structures from Chaos in a NIM Type Game
Abstract: I will discuss an ongoing research project with two 2020 Loyola grads: Ian Cowen and Zen Nguyen. We consider a modification of the famous mathematical game NIM. In our game, a state can be described as a pair of positive integers. Some states are winning, meaning if the game is in that state at your turn you can play to guarantee that you will win, and some are losing meaning no matter what you do a good player can beat you. One can figure out which are which recursively. We wrote computer code to do this for a lot of states, and plotted the losing states in the plane. The result is a shockingly complex picture with beautiful curves. We then study those curves, discussing their properties, and giving various explanations for their existence.
Rataj Lecture: Undergraduate Colloquium (Spring 2020)
When: Monday, February 24
Reception: 3:30-4:15 p.m., Palm Court, Mundelein Center
Lecture: 4:30 - 5:30pm, Cuneo 210
Speaker: Lisa Goldberg, Adjunct Professor of Economics and Statistics at UC Berkeley, Co-Director of Berkeley's Consortium for Data Analytics in Risk and Director of Research for Aperio Group.
Title: Hot Hands: What Data Science Can (and Can't) Tell Us About Basketball Trends
Abstract: Is the hot hand in basketball a real phenomenon or a cognitive illusion? I will describe a data-driven approach to this controversial question and explain how data science, despite its great contribution to sports, can go only so far in addressing some of the difficult underlying issues.
Sarah-Marie Belcastro (Director of MathILy and author of Discrete Math with Ducks) visits Loyola
- When: Wednesday, March 14, 2018
- Reception: 4:00-4:30 p.m., Mundelein 204, pies & refreshments provided
- Lecture: 4:30-5:30 p.m., Mundelein 204, Tiles on Surfaces/ Matching on Grids
- Details: calendar entry / agiaqui@luc.edu / epeters3@luc.edu
Daniel Sternheimer (Rikkyo University and Universite de Bourgogne) visits Loyola
- When: Wednesday, March 21, 2018
- Reception: 3:30-4:15 p.m., Piper Hall, refreshments provided
- Lecture: 4:30-5:30 p.m., Mundelein 204, The power of physical mathematics
- Details: calendar entry / agiaqui@luc.edu
Colloquia and Seminars (Fall 2024 / Spring 2025)
TACO Seminar:
http://gauss.math.luc.edu/algcomb/
Data Science Seminar:
https://www.luc.edu/datascience/events/datascienceseminar/
Analysis Seminar:
https://fermat.math.luc.edu/analysis_seminar/
When: October 17, 2024
Location: TBD
Time: 4:00-5:00pm
Speakers: Dr. Sven Leyffer, https://www.anl.gov/profile/sven-leyffer
Topic: Topological Design Problems and Integer Optimization
Description: Topological design problems arise in many important engineering and scientific applications, such additive manufacturing and the design of cloaking devices. We formulate these problems as massive mixed-integer PDE-constrained optimization (MIPDECO) problems. We show that despite their seemingly hopeless complexity, MIPDECOs can be solved efficiently (at a cost comparable to a single continuous PDE-constrained optimization solve). We discuss two classes of methods: rounding techniques that are shown to be asymptotically optimal, and trust-region techniques that converge under mesh refinement. We illustrate these solution techniques with examples from topology optimization.
When: September 26, 2024
Location: IES 124
Time: 4:00-5:00pm
Speakers: Sergio Alejandro Fernandez de Soto Guerrero (Graz University of Technology)
Topic: Undergraduate research
Description:
Abstract: Cumulative imaging dose to healthy tissue outside the high-dose radiation field during image-guided radiation therapy (IGRT) may increase the risk of developing complications. As such, there is a clinical need to reduce the imaging dose associated with IGRT without compromising image quality. The purpose of this study is to examine the feasibility of training a neural network to produce cone-beam computed tomography (CBCT) scans with image quality on par with current clinical usage while reducing the cumulative imaging dose to patients.
Maggie Gonzalez: Ocean robots reveal the importance of Antarctic Winter Water to the global carbon cycle.
Abstract: Antarctic Winter Water, sections of cold water trapped between relatively warm sections of water above and below it, is found across the Southern Ocean. Using data collected from floats across the Southern Ocean, we identified and characterized Winter Water and its relationship to carbon subduction, the absorption of carbon dioxide from the atmosphere into the ocean. Our findings reveal the importance of Winter Water to the global carbon cycle, allowing for improved accuracy in our understanding of the processes that contribute to climate change.
Melissa Beerbower: Lucky Sets of Fubini Rankings
Abstract: One subset of parking functions is the set of Fubini rankings, which encode the outcomes of n competitors in a race where ties are allowed. The number of lucky cars in a Fubini ranking is equivalent to the number of distinct ranks, k. We enumerate Fubini rankings and some subsets recursively through fixed sets of lucky competitors. Our enumerations explain twin coefficients for minimum powers in the lucky polynomial of l-interval Fubini rankings.
When: September 19, 2024
Location: IES 111
Time: 4:00-5:00pm
Speakers: Sergio Alejandro Fernandez de Soto Guerrero (Graz University of Technology)
Topic: MathMagic: A positroidal action over a deck of cards
Description: Positroids are a subclass of matroids born in the study of the non-negative Grassmanian by Postnikov in 2006. Since then, there have been a plethora of combinatorial objects indexing positroids, two of these being the families of decorated and bicolored permutations, which are generalizations of classical permutations. These two families can be used to study properties of positroids, and as a byproduct we end up with useful ways to describe a group action on a deck of cards. In this context, we give a definition of invariants under this group action allowing us, as an application, to develop new magic tricks with unusual ways of shuffling cards.
When: September 17, 2024
Location: IES 110
Time: 4:00-5:00pm
Speakers: Andrew Ducharme (University of Oregon)
Topic: Fourier analysis of highly oscillatory functions e^{i*t(x)}
Description: The Fourier transform is a fundamental and ubiquitous mathematical tool for writing an arbitrary function in terms of an infinite series of sines and cosines. In optics, Fourier transforms describe how light is focused by a lens. Rigorously, light traveling through an object t(x) thick is focused into bright spots whose intensities depend on the Fourier transform of e^{i*t(x)}=cos(t(x))+i sin(t(x)). These second ¿highly oscillating¿ functions are difficult to analyze, so the physics literature contains very few closed-form results regarding this class of functions. An exciting exception is known procedures for producing functions t(x) which optimize their output into exactly two, or three, or n equal beams.
Symmetric 2D outputs, like four points which are the vertices of a square, are optimized by asymmetric functions t(x,y). It is often forgotten that we do not know if the symmetric 1D functions called ¿optimal¿ are truly the best possible. I will discuss our work searching for ¿loophole¿ beamsplitters, asymmetric functions which outperform the best-known symmetric functions for optimizing intensity into n points. I will additionally show five novel highly oscillating functions we have found closed-form results for.
When: September 12, 2024
Location: IES 124
Time: 4:00-5:00pm
Speakers: Sarah Riaz, Amanda Newton, and Anurathi Madasi
Topic: Undergraduate research
Description: We will have three talks on exciting research done by our undergraduate students over the past year.
Sarah Riaz: Using Permutations to Investigating the Waffle Puzzle.
The waffle puzzle is a Wordle-type puzzle game in which you are given all the letters to make 6 words on a 5x5 board and must rearrange them by swapping only two letters at a time. This research shows some methods for getting to the solution in the least amount of swaps once we have the solution state and the number of possible types of waffles and solutions to them.
Amanda Newton: Spins of Intermediate Mass Black Holes in Galactic Nuclei From Black Hole-Star Collisions.
In galactic nuclei, black holes (BHs) collide often with stars due to the high density and velocity dispersion in this environment. In these collisions, BHs accrete mass from the stars. Because of the frequent collisions, BHs may accrete large amounts of mass, and grow into larger BHs than when formed through star death alone. We study how BH spin changes in these collisions through a simulation in order to understand the relationship between spin change and mass change in these BH-star collisions.
Anurathi Madasi: Optical and Near-Infrared Searches for Gravitational Waves: Exploring Efficiencies
The Laser Interferometer Gravitational-Wave Observatory(LIGO) is able to detect ripples in
spacetime caused by a binary black hole or binary neutron star mergers known as gravitational
waves(GW). Some of these GW events can have an electromagnetic(EM) counterpart, which can be seen optically using a telescope. This is known as multi-messenger astronomy, and having multiple sources of the same event provides insight into what the object is, where it from, etc. In our project, we aimed to test the efficiency of the Zwicky Transient Facility(ZTF) at detecting kilonovae. We populate a skymap with kilonovae, and test how many kilonovae ZTF can detect compared to how many we simulated. We updated our code from simsurvey, which is no longer being maintained, to skysurvey.
A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Those are known as generalized Fibonacci polynomials GFP. Some known examples are: Fibobacci Polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials, Vieta and Vieta-Lucas polynomials.
It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the strong divisibility property. However, this property does not hold for every second order recursive sequence. We give a characterization of GFPs that satisfy the strong divisibility property. We also give formulas to evaluate the gcd of GFPs that do not satisfy the strong divisibility property.
In the end of the talk we talk about the irreducibility of GFP. Joint work with M. Diaz-Noguera, R. Higuita, M. Romero-Rojas, R. Ramirez, and J.C. Saunders.
Colloquia and Seminars (Fall 2023 / Spring 2024)
TACO Seminar:
http://gauss.math.luc.edu/algcomb/
Data Science Seminar:
https://www.luc.edu/datascience/events/datascienceseminar/
Analysis Seminar:
https://fermat.math.luc.edu/analysis_seminar/
When: April 18, 2024
Location: IES 110
Time: 4:00-5:00pm
Speaker: Rigoberto Florez
Topic: The strong divisibility property and the resultant of generalized Fibonacci polynomials
Description: A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Those are known as generalized Fibonacci polynomials GFP. Some known examples are: Fibobacci Polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials, Vieta and Vieta-Lucas polynomials.
It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the strong divisibility property. However, this property does not hold for every second order recursive sequence. We give a characterization of GFPs that satisfy the strong divisibility property. We also give formulas to evaluate the gcd of GFPs that do not satisfy the strong divisibility property.
In the end of the talk we talk about the irreducibility of GFP. Joint work with M. Diaz-Noguera, R. Higuita, M. Romero-Rojas, R. Ramirez, and J.C. Saunders.
Bio: Dr. Florez is an Associate Professor with a Ph.D. in Mathematics from Binghamton University (SUNY). His research is in combinatorics, especially graphs and algebraically representable matroids. He is also interested in elementary number theory and enumerative combinatorics. Rigo likes working research projects with undergraduate and graduate students. His students have presented their research in local and national conferences and they have won awards doing the same. He is one of the founders of Carolina Math Seminar.
When: April 11, 2024
Location: IES 110
Time: 4:00-5:00pm
Speaker: Frank Baginski
Topic: The Shape of a High Altitude Balloon
Description: Much of the research in the upper stratosphere (35 km and above) is conducted using large scientific balloons. These balloons are not to be confused with their tiny cousins, weather balloons. The payload of a large scientific balloon can be several thousand pounds. The largest balloon is roughly 130 meters tall with a diameter of 160 meter. A typical balloon is constructed from 40 micron polyethylene (i.e., sandwich bag thickness). In the analysis of these unique structures, a number of interesting mathematical questions arise. What is the shape of the balloon at float altitude ? How is the shape designed? How is the balloon system launched? Will it deploy into the desired shape? The workhorse for NASA's Balloon Program is the (onion shaped) zero-pressure balloon. A newcomer is the (pumpkin shaped) super-pressure balloon. The answers to these and related questions lead to some interesting mathematical problems that will be discussed during the talk.
Bio: Frank Baginski received his Ph.D in Applied Mathematics from the University of Massachusetts, Amherst in 1985 and is Professor of Mathematics at George Washington University. He has collaborated with mathematicians, engineers, and physicists on modeling high altitude large scientific balloons, aerodynamic decelerators, and large-aperture reflectors.
When: February 29, 2024
Location: IES 110
Time: 4:00-5:00pm
Speaker: Claudia Solís-Lemus
Topic: Inferring biological networks
Description: Networks are graphical structures that appear in a variety of biological applications from phylogenetic networks to study evolution to interaction networks to study microbial communities in soil and plants. I will describe the novel statistical advances (and challenges) to estimate 1) phylogenetic networks from genome-wide data, and 2) microbial networks from abundance data. I will conclude with some examples of how deep learning models can be applicable to infer these types of networks.
Bio: I am an assistant professor at the Wisconsin Institute for Discovery and the Department of Plant Pathology at the University of Wisconsin-Madison. Originally from Mexico City, I did my Undergraduate degrees in Actuarial Sciences and Applied Mathematics at ITAM. Then, I did a MA in Mathematics and a PhD in Statistics at the University of Wisconsin-Madison.
When: January 29, 2024
Location: Dumbach 227
Time: 4:15-5:15pm
Speaker: Dr. Emma Zajdela
Topic: Catalyzing collaborations: Modeling scientific team formation for global impacts.
Description: I will talk about my research on modeling scientific collaboration at in-person and virtual conferences, and also include some background on my activities in science diplomacy which started while I was at Loyola and inspired this work.
Bio: Emma Zajdela is a Loyola Alum with a 2016 BS from our department. Since then she completed an MS in Applied Math from UIC and a Ph.D. in Engineering Sciences and Applied Math from Northwestern. She is now a Postdoctoral Fellow at Princeton. Her research focuses on developing mathematical models to understand and predict complex social phenomena. She has used this to study topics ranging from poker to autonomous vehicles to scientific collaboration to fashion trends.
When: December 7, 2023
Location: IES 110
Time: 4:00-5:00pm
Speaker: Elizabeth Gross, Associate Professor, Department of Mathematics, University of Hawai`i at M¿noa
Title: The Algebra and Geometry of Evolutionary Biology
Abstract: One of the main goals of evolutionary biology is to understand the evolutionary history of a set of species. These histories can aid in conservation efforts and are represented by directed graphs where the leaves represent living species and the interior nodes represent extinct species. While it is common to assume evolutionary histories are trees, when events such as hybridization are present, networks are more realistic. However, allowing for networks complicates the process of inference, and ways to overcome this complication are needed. One recent approach to phylogenetic network inference is rooted in algebra and geometry. In this talk, we discuss the role algebra and geometry has played in the statistical problems related to network inference and show how these tools combined with statistical learning can aid in network reconstruction.
When: November 16, 2023
Location: IES 124
Time: 4:00-5:00pm
Speaker: Albert S. Berahas (University of Michigan)
Title: Next Generation Algorithms for Stochastic Optimization with Constraints
Abstract: Stochastic gradient and related methods for solving stochastic optimization problems have been studied extensively in recent years. It has been shown that such algorithms and much of their convergence and complexity guarantees extend in straightforward ways when one considers problems involving simple constraints, such as when one can perform projections onto the feasible region of the problem. However, settings with general nonlinear constraints have received less attention, and many of the approaches that have been proposed for solving such problems resort to using penalty or (augmented) Lagrangian methods, which are often not the most effective strategies. In this work, we propose and analyze stochastic optimization algorithms for deterministically constrained problems based on the sequential quadratic optimization (commonly known as SQP) methodology. We discuss the rationale behind our proposed techniques, convergence in expectation and complexity guarantees for our algorithms, and present numerical experiments that we have performed. This is joint work with Raghu Bollapragada, Frank E. Curtis, Michael O'Neill, Daniel P. Robinson, Jiahao Shi and Baoyu Zhou.
About the speaker: Albert S. Berahas is an Assistant Professor in the Industrial and Operations Engineering department at the University of Michigan. Before joining the University of Michigan, he was a Postdoctoral Research Fellow in the Industrial and Systems Engineering department at Lehigh University working with Professors Katya Scheinberg, Frank Curtis and Martin Takáč. Prior to that appointment, he was a Postdoctoral Research Fellow in the Industrial Engineering and Management Sciences department at Northwestern University working with ProfessorJorge Nocedal. Berahas completed his PhD studies in the Engineering Sciences and Applied Mathematics (ESAM) department at Northwestern University in 2018, advised by Professor Jorge Nocedal. He received his undergraduate degree in Operations Research and Industrial Engineering (ORIE) from Cornell University in 2009, and in 2012 obtained an MS degree in Applied Mathematics from Northwestern University. Berahas’ research broadly focuses on designing, developing and analyzing algorithms for solving large scale nonlinear optimization problems. Specifically, he is interested in and has explored several sub-fields of nonlinear optimization such as: (i) general nonlinear optimization algorithms, (ii) optimization algorithms for machine learning, (iii) constrained optimization, (iv) stochastic optimization, (v) derivative-free optimization, and (vi) distributed optimization. Berahas is served as the vice-chair of the Nonlinear Optimization cluster for the INFORMS Optimization Society (2020-2022), the chair of the Nonlinear Optimization cluster for the INFORMS Optimization Society Conference (2021-2022), and the co-chair of the Nonlinear Optimization cluster for the ICCOPT 2022 conference (2021-2022). Berahas is the president of the INFORMS Junior Faculty Interest Group (JFIG).
When: November 7, 2023
Location: IES 111
Time: 4:00-5:00pm
Speakers: Cecily Bartsch, Cole Fleming, and Kathryn Cantrell.
Details: We will have three talks on exciting research done by our undergraduate students over the past year.
When: October 12, 2023
Location: IES 111
Time: 4:00-5:00pm
Speakers: Isabel Rentería, Amanda Newton, and Anurathi Madasi
Details: We will have three talks on exciting research done by our undergraduate students over the past year.
Colloquia and Seminars (Fall 2022 / Spring 2023)
TACO Seminar:
http://gauss.math.luc.edu/algcomb/
Data Science Seminar:
https://www.luc.edu/datascience/events/datascienceseminar/
When: Thursday, April 20, 2023
Location: IES 110
Lecture: 4:00-5:00pm
Speaker: Dr. Rebecca Willett (University of Chicago)
Title: Machine learning and data assimilation in the natural sciences and engineering
Abstract: The potential for machine learning to revolutionize scientific and engineering research is immense, but its transformative power cannot be fully harnessed through the use of off-the-shelf tools alone. To unlock this potential, novel methods are needed to integrate physical models and constraints into learning systems, accelerate simulations, and quantify model prediction uncertainty. In this presentation, we will explore the opportunities and emerging tools available to address these challenges in the context of inverse problems, data assimilation, and reduced order modeling. By leveraging ideas from statistics, optimization, scientific computing, and signal processing, we can develop new and more effective machine learning methods that improve predictive accuracy and computational efficiency in the natural sciences.
About the speaker: Dr. Willett is a Professor of Statistics and Computer Science & Director of AI at the Data Science Institute, with a courtesy appointment at the Toyota Technological Institute at Chicago. She is also the faculty lead of AI+Science Postdoctoral Fellow program. Prof. Willett’s work in machine learning and signal processing reflects broad and interdisciplinary expertise and perspectives. She is known internationally for her contributions to the mathematical foundations of machine learning, large-scale data science, and computational imaging. In addition to her technical contributions, Prof. Willett is a strong advocate for diversity in STEM and AI and has organized multiple events to support women in middle school, as undergraduate and graduate students, and as faculty members.
https://willett.psd.uchicago.edu
When: Thursday, April 13, 2023
Location: IES 110
Lecture: 4:00-5:00pm
Speaker: Rrita Zejnullahi
Title: Fund allocation for poverty alleviation
Abstract: In this talk, we consider the problem of how to optimally allocate a finite amount of resources across different locations/populations. While this decision task has wide application (e.g., allocation of health care funds to different populations, allocation of vaccines to different locations), we focus on the problem of reducing national poverty via sub-national cash transfers. Though an optimal strategy has long been identified in this situation, understanding the impact of estimation uncertainty of the needs of different groups/locations on the vector of allocations, and incorporating these into the optimal targeting procedure has not yet been formally addressed. Through simulations, we illustrate the consequences of ignoring estimation uncertainty on the vector of allocations. We then identify a strategy that formally accounts for this error. This presentation will cover work in progress.
About the speaker: Rrita Zejnullahi is a Postdoctoral Researcher in the Department of Statistics at the University of Washington, working on the development of a decision-making framework for policy decisions based on predictions from statistical models. Previously, she obtained a PhD in Statistics from Northwestern University, where she focused on small-sample methods for meta-analysis, with applications to education, medicine and the social sciences.
When: Monday, March 20, 2023
Location: IES 124
Lecture: 4:00-5:00pm
Speaker: Sarah Bockting-Conrad
Title: A Journey Toward Tridiagonal Pairs
Abstract: Tridiagonal pairs are fascinating objects with connections to many other areas of mathematics and physics. While their definition involves only linear algebra, the study of tridiagonal pairs has its origins in algebraic graph theory. In this talk, we start with some basic notions in graph theory and work our way toward showing how tridiagonal pairs arise naturally from the study of a certain special family of graphs. With this motivation in mind, we define tridiagonal pairs, discuss some of their properties, and describe their importance to algebraic graph theory.
About the speaker: Dr. Bockting-Conrad earned her PhD in Mathematics from the University of Wisconsin-Madison in 2014. She then served as a Visiting Assistant Professor at Oberlin College for one year before joining the faculty at DePaul University in 2015.
When: Thursday, December 1, 2022
Location: IES 110
Lecture: 4:00-5:00pm
Speaker: Dr. Pamela E. Harris (University of Wisconsin at Milwaukee)
Title: Multiplex juggling sequences and Kostant's partition function
Abstract: Multiplex juggling sequences are generalizations of juggling sequences (describing throws of balls at discrete heights) that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. Kostant¿s partition function is a vector function that counts the number of ways one can express a vector as a nonnegative integer linear combination of a fixed set of vectors. What do these two families of combinatorial objects have in common? Attend this talk to find out!
About the speaker: Dr. Harris is an Associate Professor in the Department of Mathematical Sciences at the University of Wisconsin at Milwaukee. She also cohosts the podcast Mathematically Uncensored and is the President and co-founder of Lathisms: Latinxs and Hispanics in the Mathematical Sciences. Her research interests are in algebra and combinatorics, particularly as these subjects relate to the representation theory of Lie algebras.
When: Thursday, November 17, 2022
Location: IES 110
Lecture: 4:00 – 5:00 p.m.
Speaker: Mena Whalen - Loyola University Chicago
Title: History of Statistics: Introductory Statistics and the People Behind It
Abstract: Learn more about how topics in introductory statistics courses came to be and the men behind the methods. This will be a lecture and discussion walking through the early 1900's following the development of Pearson, Fisher, and Neyman as researchers discovering revolutionary methods like design of experiments, chi-squared goodness of fit test, and likelihood ratio test. Come understand the context of these researchers' interactions with each other and the lasting impact they had on the field.
About the speaker: Dr. Whalen is an assistant professor of statistics in the department of mathematics and statistics at Loyola University Chicago. Her research interest includes time series analysis with an emphasis in change point analysis, spatial analysis, data science with data visualization, and network models. Special topic interest includes health policy, law and policy change, and criminology. She is an ambassador and co-organizer of the Women in Data Science (WiDS) conference for Chicago.
When: Thursday, October 20, 2022
Location: Mundelein 609
Lecture: 3:00 – 4:00 p.m.
Speaker: Michelle Yuanying Guan - DePaul University
Title: Network Models in Finance and Insurance
Abstract: The financial systems can be perceived as a complex interacting system and networks of financial institutions exhibit complex structures. In this presentation, we will show how different network structures have an impact on the spread of financial risk among financial institutions. We will also investigate how these network structures can be applied to the study of cyber risk in the insurance field.
About the speaker: Dr. Guan earned her PhD in Financial Mathematics from Florida State University in 2011. Prior to joining the faculty at DePaul University in 2020, Dr. Guan served as an Associate Professor and the Actuarial Science Advisor in the Department of Mathematics and Actuarial Science at Indiana University Northwest.
Dr. Guan is an Associate of the Society of Actuaries (ASA). Her research interests are in financial mathematics and actuarial science, focusing on heterogeneous agent models in asset pricing and systemic risk in financial systems.
When: Wednesday, September 28, 2022
Location: Cuneo 217
Lecture: 3:50 – 4:40 p.m.
Speaker: Rafael González D'León - Loyola University Chicago (Mathematics and Statistics Department)
Title: Flow polytopes as a unifying framework for some familiar combinatorial objects
Abstract: Flow polytopes are a family of beautiful geometric objects which have connections to many areas in mathematics including optimization and representation theory. Computing their volumes and enumerating lattice points of some particular flow polytopes turn out to be combinatorially interesting problems that involve beautiful enumeration formulas and many familiar combinatorial objects. Baldoni and Vergne found a series of formulas for both of these purposes, which they call Lidskii formulas, that are combinatorially powerful and pleasant. A later proof of the Lidskii formulas has been achieved by Mészáros and Morales, following the ideas of Postnikov and Stanley, using polytopal subdivisions. For a smaller class of flow polytopes, these subdivisions are triangulations that coincide with a family of framed triangulations defined by Danilov, Karzanov, and Koshevoy. These triangulations have interesting hidden combinatorial structure. We will give an introduction to flow polytopes and these formulas, including some recent applications, and a series of open problems and conjectures which we are currently working on.
About the speaker: Rafael González D'León is a mathematics professor at LUC. His research interests include enumerative, geometric, topological and algebraic combinatorics, algebraic objects supported on combinatorial structures, and the mathematics of RNA folding.
When: Wednesday, September 21, 2022
Location: BVM Hall, Room 1102
Lecture: 3:50 – 4:40 p.m.
Speaker: Emily Peters - Loyola University Chicago (Mathematics and Statistics Department)
Title: The classification of Frobenius algebras
Abstract: Frobenius algebras are both (1) a reasonably straightforward type of algebra, which in addition to a unit and multiplication also have a co-unit and co-multiplication, and (2) fundamental to the classification of 2D topological quantum fields theories (TQFTs), making them part of "baby model for quantum gravity" (according to Joaquim Kock). In this talk I will define the key players and go into detail about the classification of Frobenius algebras.
About the speaker: Professor Peters is a mathematics professor at LUC. Her research focuses on subfactors, planar algebras, and knot theory.
Tea and Colloquia (Fall 2021 / Spring 2022)
When: Thursday, March 17, 2022
Location: IES, Room 123
Lecture: 4:00 – 5:00 p.m.
Speaker: James M. Cheverud - Loyola University Chicago (Biology Department)
Title: Quantitative Genetics
Abstract: I'll talk about my field, quantitative genetics, and how evolutionary theory became mathematical. I'll also describe some challenges in the quantitative analysis revolving around negative semi-definite variance/covariance matrices.
About the speaker: Professor Cheverud is the Chair of the Department of Biology at LUC. His research focuses on evolutionary genetics, morphology, the genetics of complex traits and diseases in model organisms, and primate and mammalian evolution.
When: Thursday, December 2, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Ian Tobasco - University of Illinois at Chicago
Title: Effective Geometries in Elasticity: Wrinkles and Planar Kirigami
Abstract: What do wrinkles and shape-morphing sheets have in common? The answer is fine scale buckling — a patterned response driven by mechanical instabilities enabling macroscopic shape change beyond bulk elasticity. This talk will highlight two recent developments in the mathematics of materials leading to new predictions for (i) the zoo of wrinkle patterns that form when a shell is incompatibly confined, and (ii) the aggregate deformations of kirigami sheets made by removing a lattice of holes. Behind both advances is the concept of an “effective geometrical description” in which the underlying patterns are “averaged out”. Systematic energy minimization leads to a limiting description in which the effective geometry can be found, sometimes even by hand. Our story reminds of the classical homogenization of composites, but with fine scale buckling patterns in place of a rapidly oscillating material law. Finding effective geometries is a key step towards a mechanical theory of shape change.
About the speaker: Ian Tobasco is an Assistant Professor at the University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science. He holds a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences at New York University, and a B.S.E. in Aerospace Engineering from the University of Michigan. Tobasco works at the interface of mathematics, physics, and engineering, where advances in analysis can lead to scientific breakthroughs in the lab and vice versa. Besides elasticity, Tobasco’s current interests include the search for optimal transport mechanisms in fluid dynamics, and their comparison with naturally turbulent flows.
When: Thursday, November 18, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Jacob Michael Schauer
Title: The Statistics of Replication: Considerations and Pitfalls
Abstract: Recent research has questioned the replicability of scientific findings in various fields, including medicine, economics, and psychology. This research has also revealed that there is no standard analysis methods for replication. As a result, it is not clear how we should be designing and analyzing replication studies. This talk describes statistical considerations for studying replication, and examines their implications. It identifies some surprising statistical strengths and limitations of previous research, including the use of statistical methods with surprisingly high error rates. It then argues that such issues can be avoided in future efforts by taking into account key statistical considerations in the planning and analysis of replication studies.
About the speaker: Dr. Schauer is an Assistant Professor of Preventive Medicine at Northwestern University's Feinberg School of Medicine. His research interests include methods for studying replication, modern advances in meta-analysis, approaches to missing data, and data privacy.
When: Thursday, November 4, 2021
Location: Online (Zoom: HTTPS://LUC.ZOOM.US/J/81081283725 )
Lecture: 4:30 – 5:30 p.m.
Speaker: Hakan Demirtas (University of Illinois at Chicago)
Title: Hybrid data generation
Abstract: This talk formulates a plan for implementing a unified, general-purpose mixed data generation framework that includes nearly all major types of variables (i.e., binary, ordinal, count, and continuous) when the marginal distributions and a feasible association structure in the form of Pearson or Spearman correlations are specified for simulation purposes via a mathematically unsophisticated but effective sorting procedure.
Most relevant papers:
Demirtas, H. & Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. American Statistician, Volume 65, Issue 2, 104-109.
Demirtas, H. (2019). Inducing any feasible level of correlation to bivariate data with any marginals. American Statistician, Volume 73, Issue 3, 273-277.
About the speaker: Dr. Demirtas is an Associate Professor of Biostatistics at the Division of Epidemiology and Biostatistics in University of Illinois at Chicago. His research interests include missing data, statistical computing, multiple imputation, stochastic simulation, and random number generation
When: Thursday, October 28, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Sameer Deshpande (University of Wisconsin)
Title: Simultaneous variable and covariance selection with the multivariate spike-and-slab LASSO
Abstract: We consider multivariate linear regression models in which the goal is to predict q possibly correlated responses using a common set of p predictors. In these problems, interest lies not only in determining whether or not a particular predictor has an effect on each response but also in understanding the residual dependence between the outcomes. We propose a Bayesian procedure for such determination using continuous spike-and-slab priors. Rather than relying on a stochastic search through the high-dimensional parameter space, we develop an Expectation-Maximization algorithm targeting modal estimates of the matrix of regression coefficients and residual precision matrix. A key feature of our method is the model of our uncertainty about which parameters are negligible. Essentially, this model enables us to shrink parameters to zero in an automatic and data-adaptive fashion. Our method is seen to substantially outperform regularization competitors that employ fixed penalties on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several late-life cognitive psychological, and socioeconomic outcomes.
About the speaker: Dr. Deshpande is an Assistant Professor in Statistics Department at the University of Wisconsin - Madison. His research interests include Bayesian hierarchical modeling, treed regression, model selection, and causal inference with applications in public health and sports.
When: Thursday, October 21, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Tung Nguyen
Title: Acyclic digraphs and an algebraic construction of cospectral digraphs
Abstract: Graph theory plays a fundamental role in science and real-life applications. It is the architect for the Internet, the world wide web, biological networks, utility infrastructures, social networks, and much more.
One of the most important and interesting invariances of a graph is its spectrum which is defined as the set of eigenvalues of its adjacency matrix. The spectrum of a graph is crucial for many applications such as Google search algorithms, non-linear dynamics, controller design, data analysis, etc.
Two graphs are called isospectral if they share the same spectrum. In this talk, I will explain a new algebraic approach to the construction of isospectral graphs. This is a simple construction that has strong potential to attack some problems in the non-linear dynamics of a complex network of coupling oscillators. This is based on the joint work with Anna Krokhine, Chun Hei Lam, Ton Meesena, William Jones, John Merzel, Jan Minac, Lyle Muller through the 2021 Fields Undergraduate Summer Research Program.
Time permitting, I will briefly discuss my recent joint work and further projects with Sunil Chebolu, Jan Minac, Lyle Muller, and Federico Pasini on some exciting investigations into the spectrum of certain graphs with inspirations from representation theory.
About the speaker: Dr. Nguyen obtained his Ph.D. in 2020 from the University of Chicago with a specialty in algebraic number theory. His recent research interest includes number theory, spectral graph theory, representation theory, dynamical systems, and computational neuroscience.
When: Thursday, October 14, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Mena Whalen (Loyola University Chicago)
Title: Clustering Panels of Nonlinear Time Series Examined Though Chicago Crime During COVID-19
Abstract: When do we think that a time series will change versus when the actual change in behavior occurs is a question many researchers and policy analyst pose. Advances in change point analysis can yield a more precise estimation of a change point, where in time is a time series is changing, but how do we examine and group multiple locations together based on their change points? I propose a methodology that clusters panels of nonlinear time series with change points and point anomalies while accounting for spatial characteristics. This approach groups time series together to identify latent structures that can help researchers understand when and which areas are changing together. This methodology is applied to Chicago neighborhood crime data during the COVID-19 pandemic.
About the speaker: Dr. Whalen is an assistant professor of statistics in the department of mathematics and statistics at Loyola University Chicago. Her research interest includes time series analysis with an emphasis in change point analysis, spatial analysis, data science with data visualization, and network models. Special topic interest includes health policy, law and policy change, and criminology. She is an ambassador and co-organizer of the Women in Data Science (WiDS) conference for Chicago.
When: Thursday, September 30, 2021
Location: Mundelein Center, Room 514
Lecture: 4:30 – 5:30 p.m.
Speaker: Gregory Matthews (Loyola University Chicago)
Title: Shape-Based Classification of Partially Observed Curves with Applications to Anthropology
Abstract: We consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonparametric multiple imputation procedure; (iii) development of nearest neighbor classifiers compatible with the completion techniques. Our contributions are founded on exploiting the geometric notion of shape of a curve, defined as those aspects of a curve that remain unchanged under translations, rotations and reparameterizations. Explicit incorporation of shape information into the computational methods plays the dual role of limiting the set of all possible completions of a curve to those with similar shape while simultaneously enabling more efficient use of training data in the classifier through shape-informed neighborhoods. Our methods are then used for taxonomic classification of partially observed curves arising from images of fossilized extant Bovidae teeth, obtained from a novel anthropological application concerning paleoenvironmental reconstruction.
About the speaker: Dr. Matthews is the Director for Data Science at our Mathematics and Statistics Department. His interests include statistical disclosure control, missing data methods, statistical genetics, and statistics in sports.
When: Thursday, September 23, 2021
Location: Cuneo Hall, Room 311
Lecture: 4:30 – 5:30 p.m.
Speaker: Rafal Goebel (Loyola University Chicago)
Title: The consensus and rendezvous problems
Abstract: The consensus problem for a multi-agent system is about whether the agents (say, autonomous robots or individuals in a social network) can exchange information to reach a common opinion. A special case, known as the rendezvous problem, is about the agents asymptotically arriving at the same location. The challenges lie in the agents only being able to communicate their current opinion/location to their neighbors; in the communication structure changing over time; in constraints on the opinion/location of each agent; etc. The role of mathematics in this is, among other things, to prove that the given information structure and the chosen opinion adjustment/location control strategy works. Focusing on the rendezvous problem, the talk will show how elements of differential equations, linear algebra, graph theory, optimization, convex analysis, and switching dynamical system theory are involved in establishing convergence of the agents to the same location. The talk is based on joint work with Ricardo Sanfelice. 200-level calculus, differential equations, and linear algebra background should suffice for most of the talk.
About the speaker: Professor Goebel joined the Department of Mathematics and Statistics at Loyola University Chicago in 2008. His interests include convex, nonsmooth, and set-valued analysis; control theory, including optimal control; hybrid dynamical systems; and optimization.
Tea and Colloquia (Spring 2021)
When: Friday, April 16, 2021
Lecture: 3:00 – 4:00 p.m.
Speaker: Liubomir Chiriac (Portland State University)
Title: On the number of roots of polynomials modulo primes
Abstract: Given a polynomial with integer coefficients, we consider the number of solutions it has modulo prime numbers p. A classical problem in number theory is to study how this quantity varies with p. We will discuss several explicit examples where it is possible to give a simple rule that determines the number of linear factors in terms of seemingly unrelated objects. In the process, we will touch upon some of the very first instances of the Langlands Reciprocity Conjecture. This talk will be appropriate for undergraduate and graduate students, as well as faculty in all areas of mathematics.
Zoom link: https://luc.zoom.us/j/89406733575
Tea and Colloquia (Fall 2020)
When: Thursday, October 29, 2020 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Dr. Matthews, Professor of Statistics at Loyola University Chicago
Title: Bang the Can Slowly: An Investigation into the 2017 Houston Astros
Abstract: This manuscript is a statistical investigation into the 2017 Major League Baseball scandal involving the Houston Astros, the World Series championship winner that same year. The Astros were alleged to have stolen their opponents' pitching signs in order to provide their batters with a potentially unfair advantage. This work finds compelling evidence that the Astros on-field performance was significantly affected by their sign-stealing ploy and quantifies the effects. The three main findings in the manuscript are: 1) the Astros' odds of swinging at a pitch were reduced by approximately 27% (OR: 0.725, 95% CI: (0.618, 0.850)) when the sign was stolen, 2) when an Astros player swung, the odds of making contact with the ball increased roughly 80% (OR: 1.805, 95% CI: (1.342, 2.675)) on non-fastball pitches, and 3) when the Astros made contact with a ball on a pitch in which the sign was known, the ball's exit velocity (launch speed) increased on average by 2.386 (95% CI: (0.334, 4.451)) miles per hour.
Regular Events
For more information, follow the links to the seminar pages.
- Algebra and Combinatorics Seminar
- Analysis Seminar
- Teaching Seminar
- Undergraduate Colloquium in the Mathematical Sciences
- Statistics Seminar (see calendar)
Past Events
When: Thursday, October 22 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Wai Tong Fan, Professor of Mathematics at Indiana University Bloomington
Title: Identification and estimation for Markov processes on phylogenetic trees
Abstract: In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and branchings indicate past speciation events. Phylogenies are commonly estimated from DNA sequences collected from the species of interest. In order to obtain accurate estimates in phylogenetic analyses, it is standard practice to employ statistical approaches based on stochastic models of sequence evolution on a tree. For tractability, such models necessarily make simplifying assumptions about the evolutionary mechanisms involved. In particular, commonly omitted are insertions and deletions of nucleotides -- also known as indels. Properly accounting for indels in statistical phylogenetic analyses remains a major challenge in computational evolutionary biology. In this expository talk, we consider two fundamental questions in evolutionary biology and information theory. Namely, reconstructing the ancestral sequence and the phylogeny in a model of sequence evolution incorporating nucleotide substitutions, insertions and deletions. We shall consider the case of dense phylogenies of bounded height, which we refer to as the taxon-rich setting, where statistical consistency is achievable. We give the first polynomial-time ancestral reconstruction algorithm with provable guarantees.
When: Thursday, October 15 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Gabriel Ngwe
Title: On Computable Numbers
Abstract: A real number is said to be computable if, given a natural number n, there is a procedure that can calculate the decimal expansion accurate to n decimal places. In this talk we give an overview of computable numbers, provide examples of numbers that are not computable, and give some surprising results concerning these numbers.
When: Thursday, September 24 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Nathan Lopez
Title: A random triangle takes up 15% of its inscribing circle
Abstract: I’ll explore some applications of calculus to geometry, specifically using optimization and the average vale of a function. The talk is aimed at undergraduates who have taken or are currently taking calculus 2 or above.
When: Thursday, September 17 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Dr. Seguin, Professor of Mathematics at Loyola University Chicago
Title: Generating a Developable Surface from a Space Curve
Abstract: A developable surface is one in which near each point, there is a patch of the surface that can be flattened without distorting it. Such surfaces include cones and cylinders and appear ubiquitously in engineering applications and architectural design. Given a space curve, there are two natural ways to generate a developable surface from it. These are the so called tangent developable and rectifying developable surfaces. In my talk I’ll discuss how these correspond to endpoints of a spectrum of developable surfaces that can be constructed from a space curve. The talk will contains numerous figures to illustrate the different types of developable surfaces I’ll be discussing.
When: Thursday, September 10 | 4:30-5:30 p.m. (CT), Zoom link: https://luc.zoom.us/j/92822043616
Speaker: Dr. Tingley, Professor of Mathematics and Department Chair at Loyola University Chicago
Title: Structures from Chaos in a NIM Type Game
Abstract: I will discuss an ongoing research project with two 2020 Loyola grads: Ian Cowen and Zen Nguyen. We consider a modification of the famous mathematical game NIM. In our game, a state can be described as a pair of positive integers. Some states are winning, meaning if the game is in that state at your turn you can play to guarantee that you will win, and some are losing meaning no matter what you do a good player can beat you. One can figure out which are which recursively. We wrote computer code to do this for a lot of states, and plotted the losing states in the plane. The result is a shockingly complex picture with beautiful curves. We then study those curves, discussing their properties, and giving various explanations for their existence.
Rataj Lecture: Undergraduate Colloquium (Spring 2020)
When: Monday, February 24
Reception: 3:30-4:15 p.m., Palm Court, Mundelein Center
Lecture: 4:30 - 5:30pm, Cuneo 210
Speaker: Lisa Goldberg, Adjunct Professor of Economics and Statistics at UC Berkeley, Co-Director of Berkeley's Consortium for Data Analytics in Risk and Director of Research for Aperio Group.
Title: Hot Hands: What Data Science Can (and Can't) Tell Us About Basketball Trends
Abstract: Is the hot hand in basketball a real phenomenon or a cognitive illusion? I will describe a data-driven approach to this controversial question and explain how data science, despite its great contribution to sports, can go only so far in addressing some of the difficult underlying issues.
Sarah-Marie Belcastro (Director of MathILy and author of Discrete Math with Ducks) visits Loyola
- When: Wednesday, March 14, 2018
- Reception: 4:00-4:30 p.m., Mundelein 204, pies & refreshments provided
- Lecture: 4:30-5:30 p.m., Mundelein 204, Tiles on Surfaces/ Matching on Grids
- Details: calendar entry / agiaqui@luc.edu / epeters3@luc.edu
Daniel Sternheimer (Rikkyo University and Universite de Bourgogne) visits Loyola
- When: Wednesday, March 21, 2018
- Reception: 3:30-4:15 p.m., Piper Hall, refreshments provided
- Lecture: 4:30-5:30 p.m., Mundelein 204, The power of physical mathematics
- Details: calendar entry / agiaqui@luc.edu