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 B235 Van Vleck.
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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 | [[https://wiki.math.wisc.edu/index.php/Algebra_and_Algebraic_Geometry_Seminar_Fall_2022#Lino_Amorim Morita invariance of Categorical Enumerative Invariants | Andrei | |
| November 4th | Chris Eur | TBD | Rodriguez/Wang |
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
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.