RTG Seminar

The Thursday morning seminar will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.

If you are interested in giving a talk in this seminar, please email me at ulrich.goertz@uni-due.de or simply talk to me at some point.

Currently, the seminar is conducted online. Email ulrich.goertz@uni-due.de for the access information.

Date	Speaker	Title
5.11.2020	Nicolas Dupré	A $p$-adic analytic quantum Beilinson-Bernstein theorem
12.11.2020	Fangzhou Jin	A Gersten complex on real schemes
19.11.2020	Nils Ellerbrock	Integrality of Stickelberger elements
3.12.2020	Matteo Costantini	The Chern classes of strata of abelian differentials
10.12.2020	Robin Witthaus	tba
17.12.2020	Lennart Gehrmann	The Gross-Kohnen-Zagier theorem via $p$-adic uniformisation
7.1.2021	N. N.	tba
14.1.2021	N. N.	tba
21.1.2021	N. N.	tba
4.2.2021	N. N.	tba

Abstracts

Nicolas Dupré: A $p$-adic analytic quantum Beilinson-Bernstein theorem

Recent developments in the study of $p$-adic representations of $p$-adic groups, due to Ardakov-Wadsley among others, introduced $p$-adic analytic $\mathscr D$-modules as a tool in order to study representations geometrically. The techniques they employ revolve around p-adic analogues of the celebrated Beilinson-Bernstein localisation theorem, which roughly asserts that there is an equivalence between representations of a semisimple Lie algebra and modules over the sheaf of differential operators on the corresponding flag variety. Meanwhile, quantum group-like objects have recently been introduced in the $p$-adic setting.

In this talk, we will explain what quantum groups are and how to adapt ideas from noncommutative algebraic geometry in order to define quantum analogues of $p$-adic analytic flag varieties. We’ll then see how to obtain a Beilinson-Bernstein localisation theorem in this setup.

Fangzhou Jin: A Gersten complex on real schemes

Given a dualizing complex on a scheme, we construct a Gersten-type complex on the associated real scheme, and show that this construction establishes a bridge between coherent duality and the Verdier-type duality on real schemes. This is a joint work with Heng Xie.

Lennart Gehrmann: The Gross-Kohnen-Zagier theorem via p-adic uniformisation

The Gross-Kohnen-Zagier theorem says that certain generating series of CM points are modular forms of weight $3/2$ in the Jacobian of the modular curve $X_0(N)$.

We give a new proof of this result for quaternionic Shimura curves that admit $p$-adic uniformisation by the Drinfeld halfplane. More precisely, we give an expression for the generating series as the ordinary projection of the first derivative of a $p$-adic family of positive definite ternary theta series. This is joint work with Lea Beneish and Henri Darmon.