Sonstige Vorträge

Abstract: It is a curious fact of life in geometric topology, that the classification of closed manifolds by surgery theory becomes easier as one passes from smooth to piecewise linear and finally to topological manifolds. It was long conjectured that an even cleaner statement should be expected in the somewhat arcane world of homology manifolds of the title, which ought to fill the role of some "missing manifolds". This was finally proven by Bryant, Ferry, Mio and Weinberger in the 90's in the form a surgery sequence for homology manifolds, building on an earlier theorem of Ferry and Pedersen that any homology manifold admits a euclidean normal bundle. In the talk I will try to explain this surgery sequence, and further that its existence is incompatible with the result of Ferry and Pedersen. The latter is therefore incorrect and/or the proof of the former incomplete.

Let G be a group and R a set of elements of G with normal closure N. In general, it is not easy to understand the quotient G/N. Small Cancellation Theory is, broadly speaking, a family of conditions of the following form: Let G be a negatively curved group, R a family of ?independent enough? elements. Then G/N is itself negatively curved, and we understand many properties of this quotient. In this talk, I will review the classical Small Cancellation Theory, as well as some of its variants (Graphical Small Cancellation and Geometric Small Cancellation), and exhibit some of the groups with exotic properties that can be constructed using these methods

Abstract: Glasman proved that the category of d-excisive endofunctors on spectra is equivalent to a category of Mackey functors. In this talk, I will sketch a new proof of this together with various enhancements. Vaguely speaking, the method is to proceed by first completing a dictionary between genuine equivariant homotopy theory and Goodwillie calculus as suggested in recent work of Arone-Barthel-Heard-Sanders and then stratifying the problem accordingly. If time permits, we will also see other applications of this dictionary. This reports on work-in-progress joint with Tobias Barthel and Nikolai Konovalov.

All members of Mathematics Münster are invited to this year's Ada Lovelace Seminar.

Abstract: Homological stability is a pattern in the homology of families of spaces and groups. Examples of groups with homological stability include braid groups, symmetric groups, general linear groups, and mapping class groups. I will describe applications of this phenomenon to questions in analytic number theory. Specifically, I will report on joint work with Patzt, Petersen, and Randal-Williams on a stability pattern called uniform twisted homological stability and describe applications of these results to a conjecture of Conrey-Farmer-Keating-Rubinstein-Snaith on moments of quadratic L-functions over function fields.