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Research Seminars: Algebra and Combinatorics


Past Algebra and Combinatorics:

Fall 2017

Time & Location: All talks are on Thursdays in Norman Mayer 200-A at 12:30 PM unless otherwise noted.
Organizer: Tai Ha


September 7

Topic

Speaker - Institution

Abstract:  TBA


September 14

Topic

Speaker - Institution

Abstract:  TBA


September 21

Determinants in Wonderland

Tewodros Amdeberhan - Tulane University

Abstract

Determinants are found everywhere in mathematics and other scientific endeavors. Their particular role in Combinatorics does not need any cynical introduction or special advertisement. In this talk, we will illustrate certain techniques which proved to be useful in the evaluation of several class of determinantal evaluations. We conclude this seminar with open problem(s). The content of our discussion is accessible to anyone with "an intellectual appetite".


September 28

Involution Schubert Polynomials and Some Ordinary Schubert Polynomial Identities

Michael Joyce - Tulane University

Abstract

Abstract: Ordinary Schubert polynomials are algebraic manifestations of a certain orbit structure on the variety of complete flags. By considering two other orbit structures, we obtain involution and fpf-involution Schubert polynomials, respectively. We will discuss some of their properties and give an application for an identity involving ordinary Schubert polynomials.


October 5

Locally compact p-groups and their challenges

Karl Hofmann - TU Darmstadt and Tulane University

Abstract

Karl

 

 


October 12

Topic

Speaker - Institution

Abstract:  TBA


October 19

Lech's inequality and its improvements

Dr. Ilya Smirnov - University of Michigan

Abstract

In 1960 Lech found a simple inequality that relates the colength and the multiplicity of a primary ideal in a local ring. Unfortunately, Lech's proof also shows that his inequality is almost never sharp. After explaining the necessary background, I will present a stronger form of Lech's inequality and an even stronger conjecture that will make the inequality sharp.


October 26

Beyond Perfect Graphs: Hypercycles and Perfect Hypergraphs

Jonathan O'Rourke - Tulane University

Abstract

In attempting to extend the notion of perfect graphs to the class of hypergraphs, my research partner and I studied a class of hypergraphs which bear some resemblance to cyclic graphs.  We studied the associated primes of the cover ideals associated to this class of hypergraphs,
as well as their index of stability. This study resulted in an easy-to-describe class of hypergraphs which answer a question of Francisco, Van Tuyl, and H\`a regarding the relationship between the index of stability and the chromatic number of a family of hypergraphs, and in fact proving a stronger result.  I will explain the preliminaries necessary to understand the problem and some of the techniques used to solve it.



November 2

Topic

Speaker - Institution

Abstract:  TBA


November 9

Topic

Speaker - Institution

Abstract:  TBA


November 16

Topic

Speaker - Institution

Abstract:  TBA


November  23

Topic

Speaker - Institution

Abstract:  TBA


November 30

Topic

Speaker - Institution

Abstract:  TBA


December 7

Topic

Speaker - Institution

Abstract:  TBA



Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu