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Title:
Holonomic Poisson manifolds and deformations of elliptic algebras
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Abstract:
I will introduce the notion of holonomic Poisson manifolds, which can be thought of as a refinement of the log symplectic condition, describing "minimally degenerate" compactifications of symplectic manifolds, which we expect to arise in representation theoretic contexts. These manifolds are characterized by having finite-dimensional spaces of local deformations and quantizations. The notion is closely related to the flow of the modular vector field (a local symmetry discovered by Brylinski--Zuckerman and Weinstein, which also measures the failure of Hamiltonian flow to preserve volume). As an application, I will prove that the the first families of Feigin-Odesski elliptic algebras quantizing P^{2n} (and the corresponding Poisson structures) are universal deformations. This is joint work with Brent Pym.
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