The seminar takes place on Tuesdays, usually from 15:00 to 16:00 (German time, CET) via Zoom. The meetings start 15 minutes before the talk with a short coffee break.

The password is the first Fourier coefficient of the modular $j$-function (as digits).

Organizers:
Yingkun Li (TU Darmstadt)
Markus Schwagenscheidt (ETH Zurich)

18.01.2022 -- 16:00-17:00 (German time, GMT+1)
Isabella Negrini (McGill) A Shimura-Shintani correspondence for rigid analytic cocycles

In their paper Singular moduli for real quadratic fields: a rigid analytic approach,
Darmon and Vonk introduced rigid meromorphic cocycles, i.e. elements of
$H^1(SL_2(Z[1/p]), M^\times)$ where $M^\times$ is the multiplicative group of rigid meromorphic
functions on the p-adic upper-half plane. Their values at RM points belong to narrow
ring class fields of real quadratic fiends and behave analogously to CM values of
modular functions on $SL_2(Z)\backslash\mathbf{H}$. In this talk I will present some progress towards
developing a Shimura-Shintani correspondence in this setting.

25.01.2022 -- 15:00-16:00 (German time, GMT+1)
Márton Erdélyi (Budapest University of Technology and Economics) Matrix Kloosterman sums

We study exponential sums arosing in the work of Lee and Marklof about
the horocyclic flow on the group $GL_n$. In many cases this sum can be
expressed with the help of classical Kloosterman sums. We give effective
bounds using the very basics of cohomological methods and get a nice
illustration of the general purity theorem of Fouvry and Katz. Joint
work with Árpád Tóth.

01.02.2022 -- 15:00-16:00 (German time, GMT+1)
Vesselin Dimitrov (University of Toronto) Title: TBA