Algebra and Algebraic Geometry Seminar Fall 2022

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Here is the seminar schedule for the current term.

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Fall 2022 Schedule

date speaker title host/link to talk
October 7th TBA TBA Reserved for the arithmetic geometry workshop
October 14th Thomas Yahl Computing Galois groups of finite Fano problems Rodriguez
October 21st Lino Amorim Morita invariance of Categorical Enumerative Invariants Andrei
November 4th Chris Eur How or when do matroids behave like positive vector bundles?

(Special Location in Birge Hall 350)


(Matroids Day)

December 2 Ayah Almousa GL-Equivariant resolutions over Veronese Rings Erman/Sobieska


Thomas Yahl (TAMU)

Computing Galois groups of finite Fano problems

A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of the 27 lines on a smooth cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group that acts on these linear spaces and controls the complexity of computing them in coordinates via radicals. Galois groups of Fano problems have been studied both classically and modernly and have been determined in some special cases. We use computational tools to prove that several Fano problems of moderate size have Galois group equal to the full symmetric group, each of which were previously unknown.

Lino Amorim (KSU)

Morita invariance of Categorical Enumerative Invariants

Caldararu-Costello-Tu defined Categorical Enumerative Invariants (CEI) as a set of invariants associated to a cyclic A-infinity category (with some extra conditions/data), that resemble the Gromov-Witten invariants in symplectic geometry. In this talk I will explain how one can define these invariants for Calabi-Yau A-infinity categories - a homotopy invariant version of cyclic - and then show the CEI are Morita invariant. This has applications to Mirror Symmetry and Algebraic Geometry.

Chris Eur (Harvard)

How or when do matroids behave like positive vector bundles?

Motivated by certain toric vector bundles on a toric variety, we introduce "tautological classes of matroids" as a new geometric model for studying matroids. We describe how it unifies, recovers, and extends various results from previous geometric models of matroids. We then explain how it raises several new questions that probe the boundary between combinatorics and algebraic geometry, and discuss how these new questions relate to older questions in matroid theory.

Ayah Almousa (University of Minnesota)

GL-Equivariant resolutions over Veronese Rings

We construct explicit GL-equivariant minimal free resolutions of certain (truncations of) modules of relative invariants over Veronese subrings in arbitrary characteristic. The free modules in the resolution correspond to certain skew Schur modules corresponding to "ribbon" or "skew-hook" diagrams, and the differentials at each step are surprisingly uniform. We then utilize the uniformity of these resolutions to explicitly compute information about tensor products, Hom, and Tor between these modules and show that they also have rather simple descriptions in terms of ribbon skew-Schur modules. This is joint work with Mike Perlman, Sasha Pevzner, Vic Reiner, and Keller VandeBogert.