# Research Seminars: Algebra and Combinatorics

Past Algebra and Combinatorics:

## Spring 2018

Time & Location: All talks are on Friday in Gibson Hall 126 at 3:00 PM unless otherwise noted.
Organizer: Mahir Can

January 26

## A closed non-iterative formula for straightening fillings of Young diagram

Reuven HodgesInstitution

Abstract:

Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process, due to Alfred Young, that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. It has been a long-standing open problem to give a non-iterative, closed formula for this straightening process.

In this talk I will give such a formula, as well as a simple combinatorial description of the coefficients that arise. Moreover, an interpretation of these coefficients in terms of paths in a directed graph will be explored. I will end by discussing a surprising application of this formula towards finding multiplicities of irreducible representations in certain plethysms and how this relates to Foulkes' conjecture.

February 2

## Topic

SpeakerInstitution

Abstract: TBA

February 9

## Topic

SpeakerInstitution

Abstract: TBA

February 16

## Counting Borel Orbits in Symmetric Varieties of Types BI and CII

Ozlem UgurluTulane University

Abstract:

February 23

## De-noetherizing Cohen-Macaulay rings

Laszlo FuchsTulane university

Abstract:

The Cohen-Macaulay rings play a most important role in commutative algebra and in its applications in algebraic geometry. They are of special kind of noetherian rings, with a rich and fast developing theory. Generalizations to non-noetherian rings are scarce, none is satisfactory, since they preserve only a few selected properties of Cohen-Macaulay rings.  We introduce a new class of commutative non-noetherian rings that is a more natural generalization and enjoys the analogues of almost all of the relevant features of the classical Cohen-Macaulay theory.

The talk is based on three papers (none published as yet), one is a joint work with Luigi Salce, and another with Bruce Olberding.

March 2

## Quotients of locally compact abelian groups

Karl HofmannInstitution

Abstract:

March 8

## The Separable Quotient Problem for Topological Groups

(joint work with Sidney Morris, and Mikhail Tkachenko)

Arkady LeidermanDepartment of Mathematics, Ben-Gurion University of the Negev, Israel

Abstract: The famous Banach-Mazur problem,  which asks if  every infinite-dimensional Banach space has  an infinite-dimensional separable quotient Banach space, has remained  unsolved for 85 years, though it has been answered in the affirmative for reflexive Banach spaces and even Banach spaces which are duals. The analogous problem for locally convex spaces has been answered in the negative, but has been shown to be true for large classes of locally convex spaces including all non-normable Frechet spaces. We investigated the analogous problem of existing of separable quotients for topological groups.  Indeed there are four natural analogues: Does every non-totally disconnected topological group have a  separable quotient group which is (i) non-trivial; (ii) infinite; (iii) metrizable; (iv) infinite metrizable. All four questions are answered in the negative in our work.  However, positive answers are given for important classes of topological groups including (a) all compact groups; (b) all locally compact abelian groups; (c) all $\sigma$-compact locally compact groups; (d) all abelian pro-Lie groups; (e) all $\sigma$-compact pro-Lie groups; (f) all pseudocompact groups. We observe then that all simple algebraic groups over local fields are separable metrizable groups. Negative answers are proved for abelian precompact groups.

March 16

## Topic

Sergey GrigorianSergey Grigorian

Abstract: TBA

March 23

Pramod AcharLSU

Abstract: TBA

March 30

## Topic

SpeakerInstitution

Abstract: TBA

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