Topology @ TUM group seminar
Reading group
We usually meet Wednesdays. This semester (summer semester 2024) we are reading ``The stratified homotopy hypothesis'' by Ayala, Francis, Rozenblyum. Last semester we read Harpaz' notes on Dunn's additivity.External guests
Aug 8  Lory Aintablian (MPIM Bonn)  TBA

Aug 8  Luuk Stehouwer (Dalhousie)  TBA

July 23  Quoc Ho (Hong Kong)  HOMFLYPT homology and the categorical trace of Hecke categoriesMany interesting TQFTs can be realized as sigma models. When coupled with a sheaf theory, sigma models can be used in algebraic geometry to construct TQFTs valued in (higher) categories. With the advent of higher categorical algebra developed by Lurie and others, this perspective has been employed to great success in geometric representation theory, as exemplified, for instance, by the work of BenZvi, Gaitsgory, Nadler, and others in the various forms of the geometric Langlands program. In this talk, I will demonstrate how the study of categorified link invariants can also benefit from this point of view, using the theory of Soergel bimodules as an example. In particular, I will describe the value of the corresponding TQFT on the circle and relate it to the category of character sheaves, yielding, as a consequence, a relation between the HOMFLYPT link homology theory and coherent sheaves on the Hilbert schemes of points on $\mathbb{C}^2$ as conjectured GorskyNegutRasmussen. This is joint work with Penghui Li. The talk will be informal, requiring no background in link homology, algebraic geometry, or representation theory. 
July 15  Julian Holstein  Categorifying DonaldsonThomas invariantsTo the singularities of a hypersurface one may associate increasingly sophisticated invariants: Milnor numbers, sheaves of vanishing cycles and categories of Matrix factorizations. It is an interesting problem to globalize these locally defined invariants. The Milnor numbers associated to the moduli spaces of suitable sheaves on a CalabiYau 3fold leads to the highly influential DonaldsonThomas invariants. BravBussiDupontJoyceSzendroi have globalized the sheaf of vanishing cycles to construct a categorification of DonaldsonThomas invariants (obstructed by some orientation data). I will take about globalizing higher categorical invariants. This depends on the study of (1)shifted symplectic structures on derived schemes, but I will not expect the audience to know what those words mean. This is work in progress, joint with B. Hennion and M. Robalo. 
May  Jonte Gödicke (Hamburg) 
