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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.