Termine

Barnet-Lab, Gee, Geraghty and Taylor have shown that essentially self dual Galois representations of a totally real field on Q_p-vector spaces that are unramified almost everywhere and de Rham at p are automorphic if they are ?potentially diagonalizable?. In this talk I will explain the objects in this theorem and explain how to reprove this theorem using p-adic automorphic forms of finite slope. Unlike the previous work mentioned above, this new method generalizes to the case of CM fields.

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.

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

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.