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
F-invariants 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 Bernstein-Sato 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 Bernstein-Sato 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) A-modules of finite projective dimension? When A is commutative, it follows from the works of Bass and Gruson-Raynaud, 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 R-modules H^i_\mathfrac{m}(R/I^t) and Ext^i(R/I^t,R).
February 23rd Austyn Simpson
University of Michigan
Weakly F-regular rings can be non-catenary
Weakly F-regular 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 Cohen-Macaulay. In this talk, I will explain how in the absence of excellence, weakly F-regular rings need not be Cohen-Macaulay or even catenary. As a consequence, we extend a theorem of Ogoma concerning the existence of non-catenary 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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