Algebra and Algebraic Geometry Seminar Spring 2024

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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 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

date speaker title host/link to talk
February 16 Sean Cotner (Michigan) Schemes of homomorphisms Josh
February 23 Lingfei Yi (Minnesota) Slices in the loop spaces of symmetric varieties Dima/Josh
March 18 (Monday) Marton Hablicsek TBA Andrei/Dima
March 29 TBA TBA Josh


Sean Cotner

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.

Lingfei Yi

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.