Termine

In their seminal work, Xiao-Zhu have constructed exotic Hecke correspondences between the special fibers of different Shimura varieties, which do not necessarily lift to the generic fibers. As a consequence, they have constructed geometric realizations of the geometric Jacquet-Langlands correspondence, and verified generic instances of the Tate conjectures for certain Shimura varieties. Crucially, they only address Shimura varieties with good reduction, i.e., with hyperspecial level at a fixed prime. In these two talks, I will explain how to generalize their methods when allowing bad reduction (more precisely, when the level at a fixed prime is very special, which exists when the local group is quasi-split, but not necessarily unramified). In the first talk, I will explain how to construct exotic Hecke correspondences in these ramified situations between PEL type Shimura varieties. Combined with the "spherical" part of the categorical local Langlands correspondence, these yield new instances of the geometric Jacquet-Langlands correspondence. The key is to resolve the integral models by the splitting models of Pappas-Rapoport. In the second talk, I will define splitting versions of affine Deligne-Lustzig varieties, and explain how to study their irreducible components. Combining this with the aforementioned geometric Jacquet-Langlands correspondence, this can be used to verify generic instances of the Tate conjecture for certain Shimura varieties at very special level.

Optimal transport has become a central tool for comparing probability measures and extracting representative distributions from heterogeneous data. Yet, in many applications the objects of interest are stochastic processes, and the classical framework ignores a key structural feature: time and information. Indeed, classical Wasserstein barycenters ignore the filtration structure, making them ill-suited for problems in mathematical finance, stochastic control, and sequential decision-making. > > We study Fréchet means with respect to the adapted Wasserstein distance, where transport plans must respect the temporal flow of information. For filtered Gaussian inputs, we establish existence and characterize when the barycenter admits an ordinary Gaussian representative via a rank criterion on a local correlation matrix. We illustrate the difference between adapted and classical barycenters through numerical experiments on autoregressive processes and briefly discuss possible applications in robust stress testing of financial models. > > Based on joint work with Madhu Gunasingam, Johannes Wiesel and Ting-Kam Leonard Wong.

Seminar: AI and the Future of Mathematics (Prof. Dr. Thomas Nikolaus), A joint seminar of TRR 326, TRR 358, CRC 1442, and Mathematics Münster, devoted specifically to the impact of AI on mathematics. Programme and registration: https://www.uni-muenster.de/MathematicsMuenster/ai-math/

Let G be a normal subgroup of a group E and let Q be a characteristic quotient of G. Then, E maps to Aut(Q) and the image contains Inn(Q). This observation suggests a general strategy for obstructing normal embeddings: find a characteristic quotient Q of G such that every subgroup of Aut(Q) containing Inn(Q) has a property that pulls back through surjective homomorphisms and is incompatible with a potential ambient group E. Conclude that G does not embed as a normal subgroup of E. I will explain how tree actions of automorphism groups and low-generator metabelian quotients implement this strategy, and (time permitting) how factorization theorems for Kähler groups yield further obstructions. Applications include the following: 1. A right-angled Artin group whose finite defining graph and its complement are connected, with more than one vertex, cannot embed as a normal subgroup of Aut(F_n) or Out(F_n) for n \geq 4, or of a Kähler group. 2. If the defining graph is furthermore a tree of even diameter, the obstruction also applies to Aut(F_3), Out(F_3) and mapping class groups of possibly punctured orientable surfaces of genus at least two. 3. A group whose metabelianization is two-generated and not virtually abelian (for example F_2) cannot embed as a normal subgroup of Aut(F_n) or Out(F_n) for n \geq 3, or of those mapping class groups. 4. A finitely generated group G with b_1(G)=1 whose metabelianization is two-generated and not virtually polycyclic cannot embed as a normal subgroup of a Kähler group. This is joint work with Elia Fioravanti and Claudio Llosa-Isenrich.

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.

• 1. Adrian Celestino - Free probability, combinatorics and matrix models
• 2. Anish Chedalavada - Geometry at one level of categorification
• 3. Mahdi Haghshenas - Stability of the Expanding Universe: PDEs, Geometry, and Cosmology
• 4. Florian Riedel - Nilpotence phenomena in higher algebra
• 5. Arghya Sadhukhan - From lattices to flags: counting components via representation theory
• 6. Beatriz Salvador - From particle systems to PDEs and SPDEs
• 7. Edoardo Tolotti - Variational homogenization of the nonlinear Stokes problem

Further information

I will discuss of various curvature or spectral constraints implying that a complete Riemannian manifold of dimension 3 is diffeomorphic to the Euclidean space.