Algebra and Number Theory Seminar
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Posted September 7, 2018

Last modified September 30, 2018

Armin Straub, University of South Alabama

The congruences of Fermat, Euler, Gauss and stronger versions thereof

The Gauss congruences are a natural generalization of the more familiar Fermat and Euler congruences. Interesting families of combinatorial and number theoretic sequences are known to satisfy these congruences. Though a general classification remains wide open, Minton characterized constant recursive sequences satisfying Gauss congruences. We consider the natural extension of this question to Laurent coefficients of multivariate rational functions. One of the motivations for studying Gauss congruences lies in the fact that a certain interesting class of sequences, related to Ap'ery-like constructions of linear forms in zeta values, conjecturally satisfies stronger versions of these congruences. We outline this story and indicate recent developments. The first part of this talk is based on joint work with Frits Beukers and Marc Houben, while the second part includes joint work with Dermot McCarthy and Robert Osburn.

Applied Analysis Seminar
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Posted September 13, 2018

3:30 pm - 4:30 pm Lockett 233
Blaise Bourdin, Department of Mathematics, Louisiana State University

Variational phase-field models of fracture

Informal Geometry and Topology Seminar
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Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University

TBA

Geometry and Topology Seminar
Seminar website

Posted September 14, 2018

Last modified October 18, 2018

Scott Baldridge, LSU

A new cohomology for planar trivalent graphs with perfect matchings

Abstract: In this lecture, I will describe a simple-to-compute polynomial invariant of a planar trivalent graph with a perfect matching (think: Jones polynomial for graphs). This polynomial is interesting because of what it detects: If the polynomial is non-zero when evaluated at one, then the perfect matching is even. Such a perfect matching implies that the graph can be 4-colored. I will then show how to categorify this polynomial to get a Khovanov-like cohomology theory for planar trivalent graphs and compute a couple of simple examples. If time, I will talk about some consequences of the cohomology theory.

Colloquium
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Posted August 14, 2018

3:30 pm - 4:20 pm TBA
Hongjie Dong, Brown University

TBA