Termine

Abstract: I will report on ongoing joint work with Devalapurkar and Schlank. We construct a telescopic analog of the Beilinson fiber square, providing a simple formula for the difference between the T(n)-local K-theory of a ring spectrum R and that of its T(n-1)-localization. In fact, there is a highly structured explanation for this square in terms of the T(n)-localization of the category of noncommutative motives, which we explain. There are many applications to our understanding of redshift, of which I will discuss some. In particular, we find explicit formulas for the K(n)-local K-theory of many K(n-1)-local ring spectra in terms of Galois cohomology.

Abstract. Interesting invariants of manifolds with compact, effective, smooth torus actions (with nonempty and finite fixed points) are recorded in the respective equivariant cohomology ring. A graph-theoretical approach to the cohomology description in a wide class of GKM manifolds is given by the Chang-Skjelbred sequence. However, the resulting answer is not very convenient, because it lacks generators and relations description. This was resolved with a face ring isomorphism by M. Masuda and T. Panov in complexity n-k=0 case. The case n-k=1 was partially resolved by A. Ayzenberg, M. Masuda and myself in 2022. In particular, for GKM T^k-actions on M^{2n} with n-k>0 the problem is open, in general. In this talk I will describe a new solution to the generators and relations problem in Hamiltonian, as well as in n-k<4 cases (under some additional technical assumptions). If time permits, I will outline a construction of new GKM 8-manifolds of complexity 0 whose orbit spaces bound Brieskorn homology 3-spheres (and do not satisfy the above assumptions). This follows by producing a smooth manifold with corners structure on the respective collars (the "disks, beams, plates" construction for the smooth conical stratification on the boundary), then using the recent realization theorem of Y. Karshon and S. Kuroki. Based on arXiv 2509.00392, 2604.13629, 2608.30513.

We generalize the DeBacker--Reeder/Kaletha construction of depth-0 supercuspidal L-packets to all tame covers defined by étale cohomology. This can be seen as the "regular depth-0" part of the local Langlands correspondence for covers. This talk is based on joint work with Nhat Hoang Le, which is in turn based on earlier works by Luozi Shi and myself.

We will discuss the nonlinear stability of Schwarzschild black holes for the Einstein?massless Dirac system under spherical symmetry. In particular, we will explore how standard techniques, such as energy estimates and bootstrap arguments, can be adapted to a setting in which the matter field is more deeply coupled to the geometry than in the corresponding Einstein?scalar field system, and the energy-momentum tensor does not satisfy the positive energy condition.

In this talk, I will discuss ongoing work with R. Neagu and G. Szabó concerning weights on crossed product C*-algebras arising from actions of locally compact abelian groups. Several constructions in literature produces KMS weights or tracial weights on crossed product C*-algebras from suitable invariant weights of the underlying C*-algebra. When the acting group is the real numbers, one important such construction was introduced by Kishimoto and Kumjian. I will present new results on constructing tracial weights on crossed product C*-algebras and illustrate that these new results naturally generalize and unifies several constructions in literature, including that of Kishimoto and Kumjian. Subsequently, I will discuss the following question: under what sufficient and necessary conditions on the C*-dynamical system will all extremal tracial weights on the crossed product arises from our construction?

Kolloquium über Geschichte und Didaktik der Mathematik

Abstract: The free factor complexes (\mathrm{AF}_n) and (\mathrm{OF}_n) are built from the nontrivial proper free factors of (F_n) and their conjugacy classes, respectively, ordered by inclusion. I will discuss their model theory, with a focus on stability. In joint work with Katrin Tent, we proved that (\mathrm{AF}_2), equipped with the complement relation, is (\omega)-stable. I will then turn to higher ranks, where (\omega)-stability fails, and discuss connections with the model theory of free groups.