KU Algebra Seminar

Upcoming talks

Seminar schedule and abstracts

Thursday 10/29/2026, 2-3pm, Snow 456

Products of ideals and an extended Buchsbaum-Eisenbud-Horrocks conjecture

Craig Huneke, University of Kansas, Speaker website ↗

Abstract

About twelve years ago, I proved that in unramified regular local rings, the product of two proper ideals can never be Gorenstein unless they each have height one. I will go quickly over that proof in this talk. In that paper I also raised the question of whether or not the type of the product of two m-primary ideals in dimension d must always be at least d. In "conversations" with ChatGPT, this second question morphed into a much broader question which generalizes the famous conjecture of Buchsbaum-Eisenbud and Horrocks. I will describe this new conjecture and some results about it, as well as summarizing the recent progress on the B-E-H conjecture.

Thursday 11/12/2026, 2-3pm, Snow 456

Differential Powers of Monomial Ideals in Affine Semigroup Rings

Soumyadeep Misra, University of Kansas, Speaker website ↗

Abstract

In this talk, we discuss differential powers of monomial ideals in affine semigroup rings, including rings that are not necessarily normal. We provide explicit descriptions of these powers and use them to study their relationship with symbolic powers. In particular, we show that the symbolic and differential topologies are linearly equivalent.This is joint work with Christopher Wong.

Previous talks

Past seminar schedule and abstracts

Thursday 10/22/2026, 2-3pm, Snow 456

Poinst in projective spaces: algebra and combinatorics

Hailong Dao, University of Kansas, Speaker website ↗

Abstract

Let X be a finite set of points in projective space P^n. A question has attracted humans from antiquity (see the theorems of Pappus, Pascal, Cayley-Bacharach, etc): when can we say that X lies on a union of low degree schemes? For instance, when does X lie on a union of 2 planes? On a cubic? This question admits some simple yet beautiful answers from the algebraic and homological properties of the coordinate ring of X, but many conjectures remain. I will discuss the history of the problems and some new results, in joint works with Manik Dhar, Izabella Laba, Ben Lund and recently with Sreehari Suresh Babu.

Thursday 10/08/2026, 2-3pm, Snow 456

Elias ideals, part 2

Hailong Dao, University of Kansas, Speaker website ↗

Abstract

This is a continuation of the previous talk on Elias ideals. We will recall basic definitions and properties, discuss the "calculus of fractional ideals" that are useful for many proofs, as well as going deeper into the classification of singularities using these concepts. Examples using numerical semigroups and points in projective spaces will be presented. The new results come from an REU program conducted at VIASM, summer 2026.

Thursday 10/01/2026, 2-3pm, Snow 456

Elias ideals, part 1

Hailong Dao, University of Kansas, Speaker website ↗

Abstract

Let (R,m) be a local Cohen-Macaulay ring of dimension 1. An m-primary ideal I is called Elias if type(I) = type(R/I). This class of ideals includes those isomorphic to R or the canonical ideal (if such ideal exists). Furthermore, it is closed under inclusion. In this talk I will go through the basic properties of these ideals, and discuss how they can be related to approximately Gorenstein property, conductor of the ring and measures of singularity of R.