Date: September 2nd, 2025
Time: 2:30 - 3:30 PM
Location: BRNG 1206
Speaker: Aryaman Maithani (University of Utah)
Title: Invariant Theory of Commutative Rings
Abstract: "Given a group G acting on a ring R, we consider the subring R^G, the subring of elements fixed by G. It's a natural question to ask what "good" properties of R are inherited by R^G. Some of these questions were considered by Hilbert and Noether, and were a motivation to study noetherian rings. We will discuss some of these results. This talk should be accessible to someone who's done a first course in module theory."
Date: September 10th, 2025
Time: 12:30 - 1:15 PM
Location: LWSN B134
Speaker: Vignesh Jagathese (University of Illinois Chicago)
Title: An Introduction to F-Pure Singularities
Abstract: "In this talk we will provide a broad overview of singularities in positive characteristic. In particular, we will discuss tools to measure singularities via the Frobenius morphism, how they relate to each other, and how they recover results in characteristic 0. There will be a particular focus on F-pure singularities, or the class of rings for which the Frobenius map is a "pure" map of R-modules. Time permitting, we will discuss some asymptotic invariants in positive characteristic that measure failure of F-purity, such as the F-pure Threshold, and relate it to well known characteristic 0 invariants."
Date: September 16th, 2025
Time: 2:30 - 3:30 PM
Location: BRNG 1206
Speaker: Benjamin Mudrak (Purdue University)
Title: Licci and Glicci Monomial Ideals
Abstract: “We will discuss what is known about the linkage and G-linkage classes of monomial ideals. We will particularly focus on the results contained in the paper ‘Liaison of Monomial Ideals’ by Craig Huneke and Bernd Ulrich.”
Date: September 23rd, 2025
Time: 2:30 - 3:30 PM
Location: BRNG 1206
Speaker: Manav Batavia (Purdue University)
Title: Algebras with a Straightening Law in Invariant Theory
Abstract: "Algebras with a straightening law (ASLs) provide a striking illustration of how combinatorial methods can simplify ring-theoretic computations. In this talk, I will introduce the concept of ASLs, outline their key structural properties, and present natural examples arising as invariant rings of specific group actions."
Date: October 7th, 2025
Time: 2:30 - 3:30 PM
Location: BRNG 1206
Speaker: Joel Castillo-Rey (Basque Center for Applied Mathematics)
Title: F-Invariants and F-Singularities. Some connections
Abstract: "In this talk, we will discuss some classic results on the relationship between F-singularities and two important F-invariants – F-signature and Hilbert–Kunz multiplicity. For the F-signature, we will discuss some ideas going into the proof of Kevin Tucker's proof of existence, as well as the characterisation of regularity and strong F-regularity. For Hilbert–Kunz multiplicity, we will describe Watanabe–Yoshida conjecture and present some results illustrating the guiding philosophy that 'low Hilbert–Kunz multiplicity implies mild singularities.'"