Wigner spoke of the "the unreasonable effectiveness of mathematics in the natural sciences". This lecture series will concern "the unreasonable effectiveness of sheaves in representation theory". Nowadays, there exists dozens of examples where quantities of central importance in representation theory (dimensions, character values, Jordan-Hölder multiplicities, ...) are encoded in the stalks of interesting sheaves (intersection cohomology sheaves, ...). This establishes a fascinating connection between geometry and representation theory. In the first talk (which will be colloquium style) I will try to motivate intersection cohomology and the Decomposition Theorem via the problem of predicting the cohomology of a fibre of a map. I will then go on to introduce parity sheaves and geometric extensions (which are more recent generalizations of parity sheaves). Finally, I will explain how parity sheaves help understand several central questions in modular representation theory.

https://umich.zoom.us/j/94261794390?pwd=Z1NnNTgrVFJNSVVURkFiNkdoNXBLdz09

Meeting ID: 942 6179 4390
Passcode: UMNTRTG Speaker(s): Geordie Williamson (University of Sydney)