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Mathematics Colloquium

The UL Lafayette Mathematics Colloquium is an ongoing seminar series that features speakers from other universities and from our department. The topics cover all areas of mathematics and statistics. We try to schedule an interesting mix of topics ranging from very applied to more abstract in nature. These lectures are open to all UL Lafayette students, faculty and community members for the purpose of fostering continued discussion and networking in the various areas of mathematics.  Please contact Leonel Robert with questions or suggestions about the colloquium series.

Our colloquia are normally held on Thursday at 3:30 p.m. in room 208 of Maxim Doucet Hall. Some colloquia may be presented via zoom instead. Refreshments are served at 3:15 in room 208. To accommodate outside speakers, the colloquium is occasionally held on a different day of the week, e.g., Tuesday at 3:30, instead of Thursday.

Remember, our colloquium is open to the public and everyone who is interested is encouraged to attend.

Spring 2022 Schedule

  • 20 January 2022
    The Benson-Solomon fusion systems
    Justin Lynd
    UL Lafayette
    Abstract: A fusion system can be thought of as a "finite group at a prime p". After some historical remarks around the Classification of the Finite Simple Groups, I will explain what a p-fusion system is. Most of the examples of fusion systems we know of come from finite groups, but there do exist many exotic examples, chiefly at odd primes. In fact, we know of just one infinite family of simple exotic fusion systems at the prime 2, the Benson-Solomon fusion systems. In the second part of the talk, I will explain some coincidences that allow the Benson-Solomon systems to exist and, time permitting, discuss some of what is known about them.
  • 10 March 2022
    On Zoom. contact Leonel Robert to request the link
    Coarse geometry and rigidity
    Ilijas Farah
    York University
    Abstract: Coarse geometry is the study of metric spaces when one forgets about the small scale structure and focuses only on the large scale. For example, this philosophy underlies much of geometric group theory. To a coarse space one associates an algebra of operators on a Hilbert space, called the uniform Roe algebra. No familiarity with coarse geometry, operator algebras, or logic is required. After introducing the basics of coarse spaces and uniform Roe algebras, we will consider the following rigidity questions:
    (1) If the uniform Roe algebras associated to coarse spaces X and Y are isomorphic, when can we conclude that X and Y are coarsely equivalent?
    (2) The uniform Roe corona is obtained by modding out the compact operators. If the uniform Roe coronas of X and Y are isomorphic, what can we conclude about the relation between the underlying uniform Roe algebras (or about the relation between X and Y)?
    The answers to these questions are fairly surprising. This talk is based on a joint work with F. Baudier, B.M. Braga, A. Khukhro, A. Vignati, and R. Willett.
  • 17 March 2022
    On Zoom. contact Leonel Robert to request the link
    Acoustic and quantum scattering on the line
    Peter Gibson
    York University
    Abstract: The one-dimensional Schrödinger equation, with its connection to quantum scattering experiments, is among the most intensively studied models in quantum mechanics. This talk presents a new approach to scattering theory motivated by applications in acoustic imaging. The central idea is a natural approximation scheme that leads to new theoretical and computational methods that allow one to analyze forward and inverse scattering problems beyond the scope of previous theory. In addition, the talk will describe some newly discovered mathematical connections between scattering theory, orthogonal polynomials and a remarkable Riemannian manifold. The talk is intended for a general audience; no background in mathematical physics is required.
  • 28 April 2022
    On Zoom. contact Leonel Robert to request the link
    Infinitely many sign-changing solutions to a conformally invariant integral equation
    Mathew Gluck
    Towson University

Fall 2021 Schedule

We have a few speakers lined up already but still have room for more so let us know (contact Leonel Robert) if you want to speak or have a suggestion for a speaker. Check back for updates.

  • 14 October 2021
    On Zoom. contact Leonel Robert to request the link
    Geometries of topological groups
    Christian Rosendal
    University of Maryland
    Abstract: We will discuss how topological groups (of which Banach spaces are a particular example) come equipped with inherent geometries at both the large and small scale. In the context of Banach spaces, the ensuing study is part of geometric nonlinear analysis and we shall present various results and fundamental concepts dealing both with Banach spaces and more general topological groups appearing in analysis, dynamics and topology.
  • 15 October 2021 (1:00 pm Friday)
    On Zoom. contact Leonel Robert to request the link
    Bayesian jackknife empirical likelihood
    Yichuan Zhao
    Georgia State University
    Abstract: Empirical likelihood is a very powerful nonparametric tool that does not require any distributional assumptions. Lazar (2003) showed that in Bayesian inference, if one replaces the usual likelihood with the empirical likelihood, then posterior inference is still valid when the functional of interest is a smooth function of the posterior mean. However, it is not clear whether similar conclusions can be obtained for parameters defined in terms of U-statistics. We propose the so-called Bayesian jackknife empirical likelihood, which replaces the likelihood component with the jackknife empirical likelihood. We show, both theoretically and empirically, the validity of the proposed method as a general tool for Bayesian inference. Empirical analysis shows that the small-sample performance of the proposed method is better than its frequentist counterpart. Analysis of a case-control study for pancreatic cancer is used to illustrate the new approach.
  • 21 October 2021 (In person!)
    Almost finite almost groups
    Andrew Chermak
    Kansas State University
  • 4 November 2021 (In Person!)
    Accounting for Lack of Trust in Optional RRT Models
    Sat Gupta
    Professor and Head
    Department of Mathematics and Statistics
    University of North Carolina at Greensboro
    Abstract: When conducting face-to-face surveys containing sensitive questions, Social Desirability Bias (SDB) often leads to low response rate or worse, untruthful responding. Randomized Response Techniques (RRT) circumvent SDB by allowing respondents to provide scrambled responses. However, if respondents do not trust the RRT model, data accuracy will be compromised as shown and addressed in Young et al. (2019) and Lovig et al. (2021) for binary RRT models. Yet, no quantitative RRT model currently accounts for respondent lack of trust. We review the Young et al. (2019) and the Lovig et al. (2021) models, and propose an Optional Enhanced Trust (OET) Quantitative RRT model to mitigate respondent lack of trust by allowing additional noise to respondents who do not trust the basic Warner Additive Model. Using a combined measure of respondent privacy and model efficiency, we demonstrate both theoretically and empirically that the proposed OET model is superior to existing models.
    This talk is based on joint work with Maxwell Lovig (University of Louisiana at Lafayette), Joia Zhang (University of Washington), and Sadia Khalil (Lahore College for Women University)

Spring 2021 Schedule

  • 22 April 2021
    on Zoom at 3:30 pm -- social time at 3:00 pm contact Philip Hackney to request the link

    Informative censoring
    Gerhard Dikta
    FH Aachen University of Applied Sciences
    Based on an identifying Volterra-type integral equation for a lifetime distribution F and randomly right censored observations, we solve the corresponding estimating equation by an explicit and implicit Euler scheme. Depending on the assumptions we make about the conditional expectation of the censoring indicator given the observation time, we derive the well know Kaplan-Meier and other established estimators of F under the explicit Euler scheme. Moreover, under the implicit Euler scheme, we obtain new pre-smoothed and semi-parametric estimators of F. Some properties of the new semi-parametric estimator are discussed and a real data application finalizes the presentation.
  • 15 April 2021
    on Zoom at 3:30 pm -- social time at 3:00 pm contact Philip Hackney to request the link

    Showcase on Undergraduate Research

    This week we have four presentations by some of our undergraduate mathematics majors
    A Study of Natural Predator's Effectiveness at Controlling a Tick Population
    Maxwell Lovig
    (Faculty Advisors: Amy Veprauskas and Ross Chiquet)
    Harvesting Strategies to Control Invasive Species
    Madeleine Angerdina and Ian Bonin
    (Faculty Advisors: Amy Veprauskas and Ross Chiquet)
    Party Investment and Citizens' Willingness to Vote
    Maxwell Reigner Kane
    (Faculty Advisor: Ross Chiquet)
    Realizing Finite Groups as Internal Automorphism Groups
    Andrew Bayard
    (Faculty Advisor: Justin Lynd)

  • 8 April 2021
    on Zoom at 3:30 pm -- social time at 3:00 pm contact Philip Hackney to request the link

    Topology and Azumaya Algebras
    Ben Williams
    University of British Columbia
    The algebra Mat_d(C) of d x d matrices over the complex numbers is a familiar one. A topological Azumaya algebra of degree d is a bundle of algebras, each isomorphic to the matrix algebra, i.e., it is a twisted family of matrix algebras. I will use the algebra structure of Mat_d(C) to produce a universal example of a topological Azumaya algebra: informally, an example that is as twisted as possible.
    Classical Azumaya algebras are also twisted forms of matrix algebras, but here the twisting is purely algebraic rather than topological. They generalize central simple algebras over fields: a venerable area of study.
    Topological Azumaya algebras are intimately related to “classical" Azumaya algebras. I will attempt to explain this, and show how you can use homotopy theory to produce examples of Azumaya algebras that behave very differently from central simple algebras. This talk is intended to be accessible to a general mathematical audience.

  • 25 March 2021
    on Zoom at 3:30 pm -- social time at 3:00 pm contact Philip Hackney to request the link

    The hot spots conjecture can be false: Some numerical examples using boundary integral equations
    Jülich Supercomputing Centre
    Institute for Advanced Simulation
    The hot spots conjecture is only known to be true for special geometries. It can be shown numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.

  • 25 February 2021
    on Zoom at 3:30 pm -- social time at 3:00 pm contact Philip Hackney to request the link

    Algebraic K-theory for 2-categories
    Niles Johnson
    Ohio State University Newark
    Quillen recognized the higher algebraic K-groups of a commutative ring R as homotopy groups of a certain topological space, BGL(R)^+. We review some of the basic definitions and computations via categorical algebra. We then describe how a 2-categorical extension of this theory leads to a new model for K_3(R), together with more general applications. We will give a mild sampling of key technical details and close with some of the problems we're currently working on. The work we present is joint with Gurski-Osorno, Fontes, and Fontes-Gurski.

Fall 2020 Schedule

  • 15 October 2020
    Classification of purely infinite C*-algebras
    James Gabe
    University of Southern Denmark
    I will talk about the basics of the Elliott programme for classifying amenable (aka nuclear) C*-algebras. I will focus on the case where my C*-algebras are purely infinite.
  • 12 November 2020
    on Zoom at 3:30 pm -- social time at 3:00 pm contact Philip Hackney to request the link

    Transfer systems and weak factorization systems
    Angélica Osorno
    Reed College
    N-infinity operads over a group G encode homotopy commutative operations together with a class of equivariant transfer (or norm) maps. Their homotopy theory is given by transfer systems, which are certain discrete objects that have a rich combinatorial structure defined in terms of the subgroup lattice of G. In this talk, we will show that when G is finite Abelian, transfer systems are in bijection with weak factorization systems on the poset category of subgroups of G. This leads to an involution on the lattice of transfer systems, generalizing the work of Balchin-Bearup-Pech-Roitzheim for cyclic groups of squarefree order. This is joint work with Evan Franchere, Usman Hafeez, Peter Marcus, Kyle Ormsby, Weihang Qin, and Riley Waugh.

Spring 2020 Schedule

  • 13 February 2020
    Some applications of topology to the analysis of data
    Jose Perea
    Michigan State
    Many problems in modern data science can be phrased as topological questions: e.g., clustering is akin to finding the connected components of a space, and tasks such as regression, classification and dimensionality reduction can be thought of as learning maps between structured spaces. I will describe in this talk how tools from classical algebraic topology can be leveraged for the analysis of complex data sets. Several illustrative examples will be provided, including applications to computer vision, machine learning and computational biology.
  • 20 February 2020
    Equivalence relations and algebras of generalized matrices
    Hung-Chang Liao
    University of Ottawa
    To an equivalence relation one can naturally associate a collection of  "generalized matrices". These matrices typically have infinitely many rows and columns, but otherwise form an algebra just like ordinary matrices. Since the fundamental work of F. Murray and J. von Neumann, the study of these algebras has evolved into a huge mathematical entity with applications to many other fields. A natural and important question is how these algebras interact with the original equivalence relations. We will give an introduction to some of the most important work regarding this question, with a focus on equivalence relations arising from group actions. The talk does not assume any background beyond (the ordinary) matrix algebras, a (tiny) bit of topology, and a (tiny) bit of measure theory.
  • 12 March 2020
    The Wald Method versus The Score Method
    Jie Peng
    St Ambrose University
    The Wald method and the score method are well-known classical large sample methods of obtaining inference on parametric distributions. They are commonly used in hypothesis testing and interval estimation. In this talk, we describe these methods for finding confidence intervals and prediction intervals for the binomial, hypergeometric and Poisson distributions. For each distribution, we show via numerical comparison that the score method is better than the Wald method. The score method also provides satisfactory results even for somewhat small samples. Furthermore, We illustrate the construction of confidence intervals and prediction intervals using some practical examples.

Colloquia Archive