Tulane Home Tulane Shield logo linking to site home page

Algebra and Combinatorics 2019 Spring

Spring 2019

Time & Location: All talks are on Wednesday in Gibson Hall 310 at 3:00 PM unless otherwise noted.
Organizer: Mahir Can

January 30
Resurgence number and  Fiber Product of Projective Schemes
Sankhaneel BisuiTulane University
The symbolic powers of a homogeneous ideal  are a well-studied object. In the study of symbolic power itis natural to ask when these symbolic powers contain ordinary powers and vice versa. We can easily check that for any, n I^n \subset I^{(n)}. It is a subtle and generally open problem to determine for which positive integers m,r we have  $I^{(m)} \subset I^r  $. It is now known that for $m > Nr $ that containment holds. Now, what can be said about the bounds for a specific ideal? This question leads to the definition of resurgence number and the asymptotic versions of this number. In this talk, I will introduce the resurgence number and the asymptotic versions of the number.
Our interest is to investigate the resurgence number of fiber product of projective schemes.  We will also see how resurgence number corresponding to the ideal of the fiber product of the schemes depends on that of the original schemes. While considering the asymptotic resurgence the resurgence number of the fiber product follows a nice relation with the resurgence of the original schemes.  I am going to present the relation and we will also see how there is a possibility of the resurgence number becoming arbitrarily large.

February 6
Chudnowsky's Conjecture for a general set of points in PNk
Abu ThomasTulane University

February 27
What is WZ?
Tewodros AmdeberhanTulane University
WZ stands for Wilf-Zeilberger. We will explain the ideas behind this meta-mathematics and explore further implications, including some of our own work.

March 13
Strongly robust toric ideals
Marius VladoiuPurdue University and the University of Bucharest
Naturally,  most famous classes of toric ideals come equipped with a rich algebraic and homological structure, but they also have a common combinatorial feature, namely, equality of various special combinatorial subsets. In particular, one such class is represented by strongly robust toric ideals, for which the Graver basis is a minimal generating set. In this talk we aim to discuss a few open questions related to strongly robust toric ideals, arising from combinatorial commutative algebra, algebraic geometry, and a surprising connection to combinatorics.  The talk is based on joint works with Sonja Petrovic and Apostolos Thoma, and on an ongoing project with Apostolos Thoma.

March 20
On ideals defining products of affine schemes
Robert WalkerUniversity of Michigan
This is joint work with Irena Swanson found on arXiv:1806.03545. Given a polynomial ring C over a field and proper ideals I and J whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of I+J into a collection of primes described in terms of the associated primes of select powers of I and of J. We discuss applications to constructing primary decompositions for powers of I+J, and to attacking the persistence problem for associated primes of powers of an ideal.

March 27
The Group Algebra of a Compact  Group in the Category of Weakly Complete Vector Spaces
Karl H. HofmannTU Darmstadt