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Jonathan Weitsman, Northeastern University
We review geometric quantization in the symplectic case, and show how the program of formal geometric quantization can be extended to certain classes of Poisson manifolds equipped with appropriate Hamiltonian group actions. These include $b$-symplectic manifolds, where the quantization turns out to be finite dimensional, as well as more singular examples ($b^k$-symplectic manifolds) where the quantization is finite dimensional for odd $k$ and infinite dimensional, with a very simple asymptotic behavior, when $k$ is even.
This is a joint work with Victor Guillemin and Eva Miranda.
Final presentations from Math 9072 on the Poincaré homology sphere and related topics.
Presenters: Thomas Ng, Rebekah Palmer, Khánh Le, and Elham Mantipour.
Jonah Gaster, McGill University
Abstract: In the context of proving that the mapping class group has finite asymptotic dimension, Bestvina-Bromberg-Fujiwara exhibited a finite coloring of the curve graph, i.e. a map from the vertices to a finite set so that vertices of distance one have distinct images. In joint work with Josh Greene and Nicholas Vlamis we give more attention to the minimum number of colors needed. We show: The separating curve graph has chromatic number coarsely equal to g log(g), and the subgraph spanned by vertices in a fixed non-zero homology class is uniquely g-1-colorable. Time permitting, we discuss related questions, including an intriguing relationship with the Johnson homomorphism of the Torelli group.
There are no conferences next week.