International Seminar on Automorphic Forms
The seminar takes place Wednesdays 15:00 to 16:00 via Zoom.
The meetings start at 14:45 with a short coffee break.
You can joint the Zoom meeting at https://ethz.zoom.us/j/458512803
The password is the weight of Ramanujan's Delta function (as digits).
08.04.2020 -- 15:00-16:00
Danylo Radchenko (ETH Zurich)
Universal optimality of the E8 and Leech lattices
Abstract: I will talk about the recent proof of universal optimality of the E8 and Leech lattices (and explain what universal optimality means). While the statement itself does not involve any automorphic forms, the key ingredient in the proof is a new kind of interpolation formula for radial Fourier eigenfunctions which turns out to be intimately related to certain vector-valued modular forms for SL(2,Z). The talk is based on a joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Maryna Viazovska.
15.04.2020 -- 15:00-16:00
Paloma Bengoechea (ETH Zurich)
Periods of modular functions and Diophantine approximation
22.04.2020 -- 15:00-16:00
Jan Vonk (IAS Princeton)
Singular moduli for real quadratic fields
Abstract: In the early 20th century, Hecke studied the diagonal restrictions of Eisenstein series over real quadratic fields. An infamous sign error caused him to miss an important feature, which later lead to highly influential developments in the theory of complex multiplication (CM) initiated by Gross and Zagier in their famous work on Heegner points on elliptic curves. In this talk, we will explore what happens when we replace the imaginary quadratic fields in CM theory with real quadratic fields, and propose a framework for a tentative 'RM theory', based on the notion of rigid meromorphic cocycles, introduced in joint work with Henri Darmon. I will discuss several of their arithmetic properties, and their apparent relevance in the study of explicit class field theory of real quadratic fields. This concerns various joint works, with Henri Darmon, Alice Pozzi, and Yingkun Li.
Stephan Ehlen (University of Cologne)