Termine

Abstract

Get an insight into the research of seven new postdoctoral researchers of Mathematics Münster. In short scientific presentations they will introduce their topics.
After the talks, there will be the opportunity to exchange ideas while enjoying tea, coffee and cake in the Common Room.

I will give an introduction to Lue Pan?s approach to the study of p-adic completed cohomology of Shimura varieties, focusing on the example of quaternionic Shimura curves. I will then discuss applications to locally analytic representations of the multiplicative group of the non-split quaternion algebra over Qp. This talk is based on joint work with Zhenghui Li and Benchao Su.

Abstract: Motivated by Dieudonné theory, V. Drinfeld and E. Lau introduced a "decompletion" of the ring of Witt vectors W(R) of a derived p-complete ring R such that (R/p)_{red} is perfect, extending a construction of T. Zink. I will explain various characterizations of this decompletion (called the sheared Witt vectors) and some examples. I will also explain two applications: a conjectural description of p-divisible groups over such rings (due to Drinfeld and Lau), and a decompletion of the stack of prismatization. (Joint work in progress with Bhargav Bhatt, Vadim Vologodsky, and Mingjia Zhang, and partially also with Artem Kanaev.)

We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension 11 in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, n+1 ? 12, we prove in the same two contexts that area-minimizing hypersurfaces have at most an (n ? 10 ? ??)-dimensional singular set after an arbitrarily C?-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively. This is joint work with O. Chodosh, C. Mantoulidis and Z. Wang.

I will give an introduction to Lue Pan?s approach to the study of p-adic completed cohomology of Shimura varieties, focusing on the example of quaternionic Shimura curves. I will then discuss applications to locally analytic representations of the multiplicative group of the non-split quaternion algebra over Qp. This talk is based on joint work with Zhenghui Li and Benchao Su.