Algebra and Algebraic Geometry Seminar Spring 2024
The seminar normally meets 2:30-3:30pm on Fridays, in the room Van Vleck B317.
Algebra and Algebraic Geometry Mailing List
- Please join the AGS mailing list by sending an email to firstname.lastname@example.org 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).
Spring 2024 Schedule
|host/link to talk
|Sean Cotner (Michigan)
|Schemes of homomorphisms
|Lingfei Yi (Minnesota)
|Slices in the loop spaces of symmetric varieties
|March 18 (Monday)
Schemes of homomorphisms
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.
Slices in the loop spaces of symmetric varieties
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.