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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.

We will be meeting on Zoom until further notice. Our colloquia are normally held on Thursday at 3:30 p.m. in room 208 of Maxim Doucet Hall. 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 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
    Andreas_Kleefeld
    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