Friday, February 19, 2016 at 3:00 PM in SAS 2102
Rachel Karpman, University of Michigan
Total positivity for the Lagrangian Grassmannian
The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties, just as Young diagrams index Schubert varieties. In addition, Postnikovs boundary measurement map gives a family of parametrizations for each positroid variety. The domain of each parametrization is the space of edge weights of a weighted planar network. The positroid stratification of the Grassmannian provides an elementary example of Lusztigs theory of total nonnegativity for partial flag varieties, and has remarkable applications to particle physics. In this talk, we generalize the combinatorics of positroid varieties to the Lagrangian Grassmannian, the moduli space of maximal isotropic subspaces with respect to a symplectic form. All relevant background information on the positroid decomposition will be included in the talk.
Monday, March 14, 2016 at 3:00 PM in SAS 4201
Chris Rodger, Auburn University
Monday, April 11, 2016 at 3:00 PM in SAS 4201
Carla Savage, NC State
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