# Research Seminars: Algebra and Combinatorics

Past Algebra and Combinatorics:

## Fall 2018

**Time & Location**: All talks are on Wednesday in Gibson Hall 325 at 3:00 PM unless otherwise noted.

**Organizer**: Mahir Can

September 12

## Topic

**Speaker**Institution

**Abstract**: TBA

September 19

## Weakly complete real vector spaces

**Karl Hofmann**Tulane University

**Abstract**:

September 26

## Topic

**Speaker**Institution

**Abstract**: TBA

October 3

## Constructing a $S_n$ module for $(-1)^{n-1} \nabla p_n$

**Soumya Banerjee**Tulane University

**Abstract**:

We will outline a construction of an $S_n$ module with Frobenius characteristic $(-1)^{n-1} \nabla p_n$. The construction is realized

in two steps. First one defines an appropriate

sheaf on the Hilbert scheme of points on the plane. Subsequently, one uses Bridgeland-King-Reid correspondence to pass to $S_n$ modules.

October 10

## Topic

**Speaker**Institution

**Abstract**: TBA

October 17

## Topic

**Speaker**Institution

**Abstract**: TBA

October 24

## Associated primes of powers of edge ideals and ear decompositions of graphs (Part I)

**Ha Minh Lam**Institute of Mathematics, VAST

**Abstract**:

We give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a relationship between two seemingly unrelated notions of Commutative Algebra and Combinatorics. It covers all previous major results in this topic and has several interesting consequences.

October 31

## Associated primes of powers of edge ideals and ear decompositions of graphs (Part II)

**Ha Minh Lam**Institute of Mathematics, VAST

**Abstract**:

We give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a relationship between two seemingly unrelated notions of Commutative Algebra and Combinatorics. It covers all previous major results in this topic and has several interesting consequences.

November 7

## Topic

**Speaker**Institution

**Abstract**: TBA

November 14

## Upper bound for the regularity of powers of edge ideals of graphs. Part 1

A.V. Jayanthan |

Indian Institute of Technology, Madras
**Abstract**:

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. In this paper, we obtain an upper bound for reg(I(G)^q) in terms of certain invariants associated with G. We also prove certain weaker versions of a conjecture by Alilooee, Banerjee, Bayerslan and Hà on an upper bound for the regularity of I(G)^q and we prove the conjectured upper bound for the class of vertex decomposable graphs.

November 16

## Topic

**Speaker**Institution

**Abstract**: TBA

December 5

## On the regularity of binomial edge ideals of graphs. Part 2

**A.V. Jayanthan**Indian Institute of Technology, Madras

**Abstract**:

This will be a survey talk on regularity of binomial edge ideals of several classes of finite simple graphs. Some techniques and open problems will be discussed.