Guest seminar Algebra and Topology

The seminar usually takes place Wednesdays in F.13.11, 16:30 - 17:30.
Involved professors: Jens Hornbostel, Sascha Orlik, Britta Späth, Kay Rülling, Matthias Wendt.

 

Shigeo Koshitani: Partial answers to Puig's finiteness conjecture

One of the most important and interesting conjectures in modular representation theory of finite groups is Donovan's conjecture, due to Peter Donovan.It says that for a given finite p-group D (here p is a prime) there should exist only finitely many p-blocks B of some finite groups up to Morita equivalence such that D is a defect group of B. But in general Morita equivalence does not preserve the action of D on B (even neither of the structure of defect groups). Thus, one would like to look at stronger conjecture called Puig's finiteness conjecture, where "Morita equivalence“ is replaced by "splendid Morita equivalence" (this is the same as Puig equivalence and also source algebra isomorphism). In this talk we are going to discuss Puig's finiteness conjecture by looking at some concrete cases checked recently.

Sabrina Pauli: Tropical methods in refined enumerative geometry

Using tropical geometry one can translate problems in enumerative geometry to combinatorial problems. Thus tropical geometry is a powerful tool in enumerative geometry over the complex and real numbers. In my talk I will give an introduction to tropical geometry and explain how one can use tropical methods to solve problems in refined enumerative geometry, that is how to get a refined answer in the Grothendieck-Witt ring of a field k to enumerative problems.