Termine

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.

Abstract

A day for MM postdocs to prepare for the next step, exchange and connect with other postdocs on career-and maths-related matters.

(1) Research Statements and Proposals (with Eugen Hellmann and Angela Stevens) - A session on preparing a research statement for applications or proposals for grant applications or permanent positions: What is important, tips+tricks, which level of specificity is needed, ...
Eugen Hellmann and Angela Stevens will also both share their advice and experience on shaping the academic profile and thus bridge to the second part of the day.

(2) Scientific Profile (with Shirly Geffen and Hendrik Weber) - A session on what is important in the postdoc profiling phase.

More information and registration in September....

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.