GRK-Seminar Wintersemester 2025/26
RTG Seminar Winter term 2025/26
The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) 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.
| 16.10.2025 | Sebastian Bartling | Close local fields and fundamental lemma |
| 23.10.2025 | Georg Linden | Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane |
| 30.10.2025 | General assembly of the RTG | |
| 06.11.2025 | reserved | Mercator lecture 1 |
| 13.11.2025 | reserved | Mercator lecture 2 |
| 20.11.2025 | reserved | Mercator lecture 3 |
| 27.11.2025 | reserved | Mercator lecture 4 |
| 04.12.2025 | Carolina Tamborini | t.b.a. |
| 11.12.2025 | Thiago Solovera y Nery | The Weyl group action on Borel orbits and an affine variant |
| 18.12.2025 | Sally Gilles | t.b.a. |
| 08.01.2026 | Julian Quast | The trianguline variety for reductive groups |
| 15.01.2026 | N.N. | t.b.a. |
| 22.01.2026 | N.N. | t.b.a. |
| 29.01.2026 | N.N. | t.b.a. |
| 05.02.2026 | N.N. | t.b.a. |
Abstracts
Sebastian Bartling: Close local fields and fundamental lemma
I want to explain how to put Rapoport-Zink spaces and their function field versions due to Hartl-Viehmann into a profinite family using the philosophy of close local fields. In this setting, one can show that certain arithmetic intersection numbers stabilize in these families and as an application one deduces Wei Zhang’s Arithmetic Fundamental Lemma in the function field case by reducing into to the known p-adic case. This is joint work with Andreas Mihatsch.
If time permits, I will explain how similar ideas when applied to the Witt-vector affine Grassmannian, Witt-affine Springer fibers and Affine Deligne-Lustzig varieties should imply also the Fundamental Lemma for stable base change in the function field case by reducing it to the known p-adic case. This is joint work, very much still in progress, with Kazuhiro Ito and Andreas Mihatsch.
Georg Linden: Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane
We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $GL_2(F)$ and for some of its subgroups. This extends a recent classification of torsion equivariant line bundles with connection due to Ardakov and Wadsley, but our approach is somewhat different. A crucial ingredient is a construction due to Van der Put which relates invertible analytic functions on the Drinfeld upper half plane to currents on the Bruhat-Tits tree. Another tool we use is condensed group cohomology.