Sonstige Vorträge

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.

By a connection with a formal parameter, we mean a connection on a scheme $X$ that is relatively smooth over the ring $R = k[[t]]$, where $k$ is a field of characteristic $0$. The monodromy of such a connection is a flat affine group scheme over $R$. We introduce the notion of prudent group schemes in terms of their representations; this property turns out to be equivalent to the projectivity of the coordinate ring (a result that holds over any complete DVR). In this talk, we discuss the question: When is the monodromy group of a connection prudent? Our main tool is the concept of hyper-prudence, which involves the $t$-adic completion of the representation category. This is a joint work with J.P. dos Santos (Montpellier) and Dao Van Thinh, Pham Thanh Tam (Hanoi).

We invite all early career researchers who have started their position at Mathematics Münster in 2026 to join us for a welcoming Meet&Greet session with the Cluster spokespersons, some investigators, the MM management staff and all the new members.