Leonid Rybnikov (Universit茅 de Montr茅al)
Title: Cactus flower curves, integrable systems, and crystals.
Abstract: The moduli space of rational curves with n+1 marked points and a tangent vector (called framing) at the last of them has a natural compactification F_n analogous to the Deligne-Mumford one for the space of non-framed curves, called moduli space of cactus flower curves.
Contrary to the usual Deligne-Mumford compactification, it is singular
-- but still has many nice properties. I will explain how this space arises as the parameter space for some remarkable family of quantum integrable systems (namely, for Gaudin degenerations of the XXZ Heisenberg spin chain). On the other hand, the fundamental group of the real locus of this moduli space, called virtual cactus group, controls coboundary monoidal categories that are finitistic and concrete (i.e.
endowed with a faithful monoidal functor to finite sets). This describes the monodromy of solutions to Bethe ansatz in the Gaudin integrable systems in terms of the commutor operation on tensor products Kashiwara crystals. This is a joint work (partially in progress) with Aleksei Ilin, Joel Kamnitzer, Yu Li, and Piotr Przytycki.
Location: UQAM PK-5675