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 email@example.com or simply talk to me at some point.
Currently, the seminar is conducted online. Email firstname.lastname@example.org for the access information.
|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|
|17.12.2020||Lennart Gehrmann||The Gross-Kohnen-Zagier theorem via $p$-adic uniformisation|
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.