Commutative Algebra Seminar

Fall 2021, Tuesdays 2:00 pm, LCB 222

Every other week, we will attend the Fellowship of the Ring virtual seminar, hosted by MSRI

Date Speaker Title — click for abstract
August 31 Fellowship of the ring
Bernd Sturmfels
Virtual seminar
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September 14 Fellowship of the ring
Wenliang Zhang
Virtual seminar
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September 28 Fellowship of the ring
Steven Sam
Virtual seminar
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October 12 Fellowship of the ring
Yairon Cid-Ruiz
Virtual seminar
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October 26 Fellowship of the ring
Julia Pevtsova
Virtual seminar
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November 2 Eamon Quinlan-Gallego
University of Utah
Bernstein-Sato theory in positive characteristic
Given a holomorphic function f, its Bernstein-Sato polynomial is a classical invariant that detects the singularities of the zero locus of f in very subtle ways; for example, its roots recover the log-canonical threshold of f and the eigenvalues of the monodromy action on the cohomology of the Milnor fibre. In this talk I will describe a characteristic-p analogue of this invariant and some recent developments that I proved in my thesis. I will also describe some open problems and future directions that I am working on at the moment.
November 9 Fellowship of the ring
Patricia Klein
Virtual seminar
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November 16 Vaibhav Pandey
University of Utah
Are natural embeddings of determinantal rings split?
Over an infinite field, a generic determinantal ring is the fixed subring of an action of the general linear group on a polynomial ring; this is the natural embedding of the title. If the field has characteristic zero, the general linear group is linearly reductive, and it follows that the invariant ring is a split subring of the polynomial ring. We determine if the natural embedding is split in the case of a field of positive characteristic. Time permitting, we will address the corresponding question for Pfaffian and symmetric determinantal rings. This is ongoing work with Mel Hochster, Jack Jeffries, and Anurag Singh.
November 23 James Cameron
University of Utah
Local cohomology modules of group cohomology rings
For G a finite group and k a field of characteristic dividing |G| there is a rich history of studying the geometry and commutative algebra of the group cohomology ring of G with coefficients in k. These rings are complicated, but some of their geometric features can be described in group theoretic terms. These geometric features can often be phrased in terms of local cohomology. I will survey some of the results around local cohomology modules of group cohomology rings, and describe how to study these modules using a topological perspective. I will also mention some open problems.
November 30 Fellowship of the ring
Robin Baidya
Virtual seminar
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December 7 Selvi Kara
University of Utah
Blow-Up algebras of strongly stable ideals
Let A be a polynomial ring and I_1,..., I_r be a collection of ideals in A. The multi-Rees algebra of I_1,..., I_r encode many algebraic properties of these ideals, their products, and powers. Additionally, the multi-Rees algebras arise in successive blowing up of Spec(A) at the subschemes defined by I_1,..., I_r. Due to this connection, Rees and multi-Rees algebras are also called blow-up algebras in the literature.

In this talk, we will focus on Rees and multi-Rees algebras of strongly stable ideals. In particular, we will discuss the Koszulness of these algebras through a systematic study of these objects via three parameters: the number of ideals in the collection, the number of Borel generators of each ideal, and the degrees of Borel generators. In our study, we utilize combinatorial objects such as fiber graphs to detect Gröbner bases and Koszulness of these algebras. This talk is based on a joint work with Kuei-Nuan Lin and Gabriel Sosa.

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Archive of older seminars

This web page is maintained by Srikanth Iyengar, Karl Schwede, Anurag K. Singh.