Veranstaltungen am Mathematischen Institut

There will be 8 speakers, each will have 5 minutes for a blackboard talk and 2 minutes to answer 1-2 questions from the audience. The line-up and titles are follows: 1. Arthur Bartels: K-theory of Hecke algebras 2. Konrad Bals: The Topological Cartier--Raynaud Ring 3. Johannes Ebert: Tautological classes and higher signatures 4. Robert Szafarczyk: Number rings over the sphere spectrum 5. Edith Hübner: Animated lambda-rings and Frobenius lifts 6. Michael Weiss: The diffeomorphism group of an exotic sphere 7. Devarshi Mukherjee: Bivariant homotopy algebraic K-theory 8. Thomas Nikolaus: Maps between spherical group rings

Central sequences play a fundamental role in operator algebras, from property Gamma and the MacDuff property for II_1 factors to characterizations of tensorial absorption for C*-algebras, for example. Given the deep link between operator algebras and dynamics, it is natural to look for dynamical analogues of central sequence properties. This turns out to be subtle. In joint work with Grigorios Kopsacheilis, Hung-Chang Liao, and Andrea Vaccaro, a central sequence property (uniform property Gamma) is shown to be equivalent to a topological dynamical property (the small boundary property). I will discuss a body of work related to these ideas.

Abstract: The space of all smooth hypersurfaces of a given degree in a complex projective variety is itself a variety. I will explain how to understand some of its cohomology using tools from homotopy theory: smooth hypersurfaces are given by holomorphic sections of line bundles subject to a differential condition, and these can be compared to continuous sections of appropriate jet bundles. This strategy usually goes under the name of "h-principle", and we will see an algebraic instance of that. I will also explain some consequences: a cohomological stability phenomenon, and a relation to classifying spaces of diffeomorphism groups of hypersurfaces.