Algebra and Algebraic Geometry Seminar Fall 2022
The Seminar takes place on Fridays at 2:30 pm, either virtually (via Zoom) or in person in room B325 Van Vleck.
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 Please join the AGS mailing list by sending an email to ags+join@ggroups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).
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) 
Rodriguez/Wang 

December 2  Ayah Almousa  GLEquivariant resolutions over Veronese Rings  Erman/Sobieska 
Abstracts
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
CaldararuCostelloTu defined Categorical Enumerative Invariants (CEI) as a set of invariants associated to a cyclic Ainfinity category (with some extra conditions/data), that resemble the GromovWitten invariants in symplectic geometry. In this talk I will explain how one can define these invariants for CalabiYau Ainfinity 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)
GLEquivariant resolutions over Veronese Rings
We construct explicit GLequivariant 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 "skewhook" 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 skewSchur modules. This is joint work with Mike Perlman, Sasha Pevzner, Vic Reiner, and Keller VandeBogert.