UCSD Number Theory Seminar (Math 209)

Thursdays 2-3pm PST, APM 6402 and virtually

We will run a "hybrid" seminar this quarter, where we meet in the seminar room and simultaneously over Zoom. The Zoom meeting code is 993 5967 5186; the password is the four-digit number of the meeting room.

Most talks will be preceded by a "pre-talk" meant for graduate students and postdocs, starting 40 minutes before the announced time for the main talk and lasting about 30 minutes. Pre-talks are also available via Zoom.

Don't forget to register for Math 209 if you are a UCSD graduate student. Continued department financial support for this seminar is contingent on maintaining sufficient enrollment.

The organizers strive to ensure that all participants in this seminar enjoy a welcoming environment, conducive to the free expression and exchange of ideas. In particular, the pre-talks are meant to provide a safe space for junior researchers to ask questions of the speaker. All participants are expected to cooperate with this effort and encouraged to contact the organizers with any concerns.

To subscribe to our weekly seminar announcement, or to join the number theory group's Zulip discussion server for additional announcements, please contact the organizers. (Thanks to Zulip for providing Sponsored Cloud Hosting for this server.)

As of spring 2020, this site is dynamically generated from researchseminars.org, which see for other seminars worldwide (or for this seminar listed in your local timezone).

Fall Quarter 2023

For previous quarters' schedules, click here.

September 28

Organizational meeting (no Zoom)

October 5

Aaron Pollack (UC San Diego)
Arithmeticity of quaternionic modular forms on G_2

Quaternionic modular forms (QMFs) on the split exceptional group G_2 are a special class of automorphic functions on this group, whose origin goes back to work of Gross-Wallach and Gan-Gross-Savin. While the group G_2 does not possess any holomorphic modular forms, the quaternionic modular forms seem to be able to be a good substitute. In particular, QMFs on G_2 possess a semi-classical Fourier expansion and Fourier coefficients, just like holomorphic modular forms on Shimura varieties. I will explain the proof that the cuspidal QMFs of even weight at least 6 admit an arithmetic structure: there is a basis of the space of all such cusp forms, for which every Fourier coefficient of every element of this basis lies in the cyclotomic extension of Q.

November 16

Tony Feng (UC Berkeley)