Seminar Darstellungstheorie

Das Seminar Darstellungstheorie findet normalerweise dienstags, 14.15 - 15.15 Uhr in G.13.18 statt.

Beteiligte Dozenten: Sascha Orlik, Kay Rülling, Tobias Schmidt, Britta Späth.

Zhixiang Wu: Bernstein--Zelevinsky duality for locally analytic principal series representations

Bernstein--Zelevinsky duality is classically a duality on the derived category of smooth representations of a p-adic Lie group. In this talk, we will consider the Bernstein--Zelevinsky duality for locally analytic representations of p-adic Lie groups, and compute explicitly the duality for principal series representations. This is joint work with Matthias Strauch.

Erik Barinaga: On Chow groups of Deligne--Lusztig varieties

Deligne--Lusztig varieties play a very important role in the representation theory of finite groups of Lie type, as covered in the landmark 1976 paper by Deligne and Lusztig. Nevertheless, these schemes remain mysterious in general. For instance, as of yet we have no real strategy to determine their l-adic cohomology groups in a coherent way, especially outside of the general linear case, or small rank examples. Likewise, not much is known about their Picard groups or more general (higher) Chow groups. In this talk, we will present some results on (rational, higher) Chow groups of Deligne--Lusztig varieties. We discuss a recursive formula describing the rational Picard group of a Deligne--Lusztig variety in terms of a smaller variety in the case of G=Gl_n. If time permits, we also discuss the integral Picard group of some fixed Weyl group elements. This is work in progress, and part of my PhD thesis.

James Taylor: Categories of Equivariant Vector Bundles on Drinfeld Symmetric Spaces

In this talk we will describe various categories of equivariant vector bundles and vector bundles with connection on Drinfeld symmetric spaces. These include the category of G^0-finite ("torsion") vector bundles with connection and the category of Lubin-Tate bundles introduced by Kohlhaase.

Tommy Lundemo: On the residue sequence in logarithmic THH

While algebraic K-theory, TC, and THH all enjoy a common localization property, a key tool to study the resulting cofiber sequences - dévissage - is only available for algebraic K-theory. There have been two major attempts to circumvent this: The first, due to Hesselholt--Madsen and Blumberg--Mandell, involves a model of THH and TC of Waldhausen categories that produces new localization sequences as an instance of Waldhausen's fibration theorem. The second, due to Rognes--Sagave--Schlichtkrull, bypasses dévissage entirely. Instead, they use Rognes' logarithmic THH to generalize a classical residue sequence involving logarithmic differential forms to a cofiber sequence of cyclotomic spectra.

I will report on work in progress, in which I will address the problem of reconciling the localization property of THH with that of its logarithmic counterpart. When combined with forthcoming work of Ramzi--Sosnilo--Winges, this becomes closely related to the problem of realizing logarithmic THH as the THH of a stable infinity-category, providing a candidate category of "logarithmic modules" in specific cases.

Ting-Han Huang: On the p-adic Gross–Zagier formula for triple product p-adic L-functions attached to finite slope families

We will briefly explain the work in the thesis (and a recent paper with A. Kazi) of the speaker, which revolves around the p-adic Gross–Zagier formula for (twisted) triple product p-adic L-functions attached to finite slope families. Such a formula relates the values outside the interpolation range to certain p-adic Abel–Jacobi map images, and serves as a crucial ingredient to study the Bloch–Kato conjecture or special case of BSD-conjecture. We will skip the geometric part of the story and focus instead on the computation of the polynomial q-expansions. In the end, we will demonstrate the relation between the special values of p-adic L-functions and the p-adic Abel–Jacobi images of diagonal cycles.

• Seminare vergangener Semester