PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Calder Daenzer, Mari Royer, Nigel Higson, Mathieu Stienon, Ping Xu.

Title:Splitting Problem for Homogeneous Supermanifolds
Seminar:GAP Seminar
Speaker:Elizaveta Vishnyakova, University of Luxembourg
Abstract:
A supermanifold is called split if it is isomorphic to a vector bundle with a purely even base and purely odd fiber. In the smooth category, all supermanifolds are known to be split (although non-canonically). In contrast, complex-analytic supermanifolds are not necessarily split, see for example the moduli space of super Riemann surfaces of genus $g>4$ (R.Donagi and E.Witten). The talk is devoted to the splitting problem for complex homogeneous spaces. While any complex Lie supergroup G is split, there are examples of non-split complex homogeneous supermanifolds. In fact, almost all flag supermanifolds are non-split. The main question that we will discuss is how to determine if a given complex homogeneous supermanifold is split or non-split. Our results will be illustrated on super Grassmannians.

Room Reservation Information

Room Number:MB106
Date:12 / 10 / 2013
Time:02:30pm - 03:30pm