Commutative Algebra Seminar
Spring 2024, Friday 2:00–3:00 pm, LCB 215
Date  Speaker  Title — click for abstract 
January 12th  Trevor Arrigoni University of Kansas 
Finvariants of simple algebroid plane branches
Frobenius thresholds are a family of invariants associated to singularities in positive characteristic. Though originally defined in terms of the splitting properties of Frobenius,
Mustaţă, Takagi, and Watanabe showed in 2005 that Frobenius thresholds are closely related to the BernsteinSato polynomial and other invariants of singularity in characteristic zero. In this
talk, we will present algorithms to compute Frobenius thresholds of a natural family of irreducible power series in two variables. These algorithms look at computing Frobenius thresholds as an
integer programming problem. The integer programs discussed here build upon those recently developed by Hernández and Witt to compute the roots of the BernsteinSato polynomial for this family
of curves.

January 19th  No seminar 
TBA

January 26th  No seminar 
TBA

February 2nd @2:30, (note unusual time) 
Souvik Dey Charles University 
Finitistic dimension and singularity categories
Let A be a Noetherian ring (not necessarily commutative). When is there a uniform
upper bound on the projective dimensions of all (left) Amodules of finite projective
dimension? When A is commutative, it follows from the works of Bass and GrusonRaynaud, that
this is the case if and only if A has finite Krull dimension. The question of whether such a
uniform upper bound exists for Artin algebras, even when restricted to finitely generated
modules only, was first publicized by Bass in the 1960s. This question, since known as the
finitistic dimension conjecture, remains open even after half a century. In this talk, based on
ongoing joint work with Jan Stovicek, we will present some criteria for the existence of such
uniform upper bounds in terms of certain form of generation in singularity categories. One
ingredient of our approach is based on a generalization of the "delooping level" of GĂ©linas.

February 9th  Nursel Erey Gebze Technical University 
Regularity and Normalized Depth Function of Squarefree Powers
Let I be a monomial ideal. The k'th squarefree power of $I$ is the ideal generated by the squarefree monomials in I^k. In this talk, we investigate the regularity and depth
function of squarefree powers and consider the question of when such powers have linear resolution.

February 16th  Hunter Simper University of Utah 
Annihilators of local cohomology of determinantal thickenings
Let I be the maximal minors of generic matrix X in R=\mathbb{C}[X]. In this talk I will discuss the module
structure, in particular that annihilators, of the Rmodules H^i_\mathfrac{m}(R/I^t) and Ext^i(R/I^t,R).

February 23rd  Austyn Simpson University of Michigan 
Weakly Fregular rings can be noncatenary
Weakly Fregular rings (i.e. Noetherian rings in which all ideals are tightly closed) are among the mildest singularity types in prime characteristic commutative algebra. They are always normal, and under excellent hypotheses are CohenMacaulay. In this talk, I will explain how in the absence of excellence, weakly Fregular rings need not be CohenMacaulay or even catenary. As a consequence, we extend a theorem of Ogoma concerning the existence of noncatenary splinters of equal characteristic zero to prime characteristic. This is joint work with Susan Loepp.

March 1st  Daniel McCormick University of Utah 
TBA
TBA

March 8th  Spring break No seminar 

March 14th (unusual day) LCB 222 (unusual room) 
Rankeya Datta University of Missouri 
TBA
TBA

March 15th  Prashanth Sridhar Auburn University 
TBA
TBA

March 22nd  TBA TBA 
TBA
TBA

March 29th  Emily Witt University of Kansas 
TBA
TBA

April 5th  TBA TBA 
TBA
TBA

April 12th  TBA TBA 
TBA
TBA

April 19th  TBA TBA 
TBA
TBA

April 26th  TBA TBA 
TBA
TBA

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