Mathematics Home / Algebra and Combinatorics 2018 Fall

Fall 2018

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

Organizer: Mahir Can

**September 19**

Weakly complete real vector spaces

Karl HofmannTulane University

Abstract:

**October 3**

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

Soumya BanerjeeTulane 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 24**

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

Ha Minh LamInstitute 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 LamInstitute 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 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 21**

Thanksgiving

**December 5**

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

A.V. JayanthanIndian 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.