Featured Speaker: Hannah Larson (Stanford)

Title: Chow rings of low-degree Hurwitz spaces.

Abstract:
The Chow ring of a variety packages information about its subvarieties and how they intersect (a sort of "algebraic version" of the cohomology ring). When studying Chow rings of moduli spaces, there are often certain "tautological" classes that arise naturally from the moduli problem. While determining the full Chow ring of a moduli space may be difficult, the subring generated by tautological classes may have a nicer structure. This motivates two questions: (1) What is the structure of the tautological ring? (2) To what extent are all classes tautological? I'll start by giving some background about these questions for the moduli space of curves M_g, and explain how they also motivated us to study Hurwitz spaces H_{k,g}, parametrizing degree k, genus g covers of P^1. Then, I'll give some results addressing (1) and (2) for the Hurwitz spaces H_{k,g} for k \leq 5. This is joint work with Samir Canning.

Seminar Covid Statement
A notice to non-MIT seminar participants: at this time, not all seminars are open to the general public, and access to the MIT campus is highly regulated. Please check the seminar webpage or with the event organizer and confirm whether the seminar you'd like to attend is open to non-MIT (i.e. without CovidPass) attendees.
Some seminars may offer a Zoom option for off-campus participants.
To access MIT buildings for a math seminar without MIT's CovidPass, you must be invited via a Tim Ticket ahead of time. There are no exceptions; please make sure to plan accordingly before coming to campus. To be able to activate the Tim Ticket, the attendee will need to submit an attestation about vaccination and health status and provide contact info.
Finally, a reminder to all in-person participants. MIT Covid policies must be adhered to: remember to keep your mask on while inside buildings, eating food is not allowed within lecture rooms, and if you are feeling sick on the day of the talk, please stay home!