Seminar
The CCAC runs a virtual seminar series on recent results in combinatorial commutative algebra. All are welcome to join. Further information is given below. Join our mailing list to learn about upcoming talks.
Next Talk
We are taking a short break for the summer, but will return in Fall 2024.
Upcoming Talks
Stay Tuned!!!
Past Talks
Associate Professor, Texas State University
DATE: April 9, 2024
TIME: 11:30 EST
TITLE: Tropical Type Ideals with an Application to Toric Edge Rings of Bipartite Graphs
ABSTRACT: A tropical hyperplane can be thought of as an affine shift of the normal fan of a simplex in R^d. A collection of such objects decomposes the ambient space into regions that have natural monomial labelings given by "type" data. We study the resulting type ideals, in the process providing minimal cellular resolutions, and also relating certain initial ideals to Stanley-Reisner ideals of root polytopes. We focus especially on applications to toric edge rings of bipartite graphs, where we establish new results regarding regularity, as well as provide new "tropical" proofs of known results. This is joint work with Ayah Almousa and Ben Smith
Assistant Professor, Universidad de los Andes
DATE: March 4, 2024
TIME: 11:30 EST
TITLE: Castelnuovo-Mumford Regularity of Symbolic Powers of Cover Ideals of Graphs
ABSTRACT: Let G be a graph. The cover ideal J(G) of G is the ideal generated by squarefree monomials corresponding to vertex covers of G. One can also define this ideal as the Alexander dual of the edge ideal of G. In this talk we review the recent results about the Castelnuovo-Mumford regularity of symbolic powers of cover ideals. In particular, we characterize all graphs G with the property that J(G)^(k) has a linear resolution for some (equivalently, for all) integer k >= 2. Here J(G)^(k) denotes the k-th symbolic power of J(G).
Associate Professor, Gebze Technical Univ.
DATE: February 13, 2024
TIME: 11:30 EST
TITLE: Squarefree Powers of Edge Ideals
ABSTRACT: Let I be a monomial ideal. The k'th squarefree power of I is generated by the squarefree monomials in I^k. In this talk, we discuss some results and conjectures about the regularity and the depth function of squarefree powers of edge ideals.
SLIDES: Click here for a copy of the slides
Professor, Tulane University
DATE: January 23, 2024
TIME: 11:30 EST
TITLE: Binomial Expansion for Rational Powers and Integral Closures of Sums of Ideals
ABSTRACT: Let A and B be algebras over a field k. Let I and J be nonzero proper ideals in A and B, respectively. We investigate the question of when a binomial expansion for rational powers of I+J (considered as an ideal in A (x)_k B) exists. This question is motivated from the facts that similar expansions were known to exist for symbolic powers and adjoints of I +J.