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From Symplectic to Poisson manifolds and back

Connections Workshop: Noncommutative Algebraic Geometry February 01, 2024 - February 02, 2024

February 01, 2024 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Eva Miranda (Polytechnical University of Cataluña (Barcelona))
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

From Symplectic to Poisson manifolds and back

Abstract

b-Structures and other generalizations (such as E-symplectic structures) are ubiquitous and sometimes hidden, unexpectedly, in a number of problems including the space of pseudo-Riemannian geodesics and regularization transformations of the three-body problem. E-symplectic manifolds include symplectic manifolds with boundary, manifolds with corners, compactified cotangent bundles and regular symplectic foliations. Their deformation quantization was studied à la Fedosov by Nest and Tsygan. How general can such structures be? In this talk, I first explain how to associate an E-symplectic structure to a Poisson structure with transverse structure of semisimple type (joint work with Ryszard Nest) and I will connect this to a result by Cahen, Gutt and Rawnsley on tangential star products. This result illustrates how E-symplectic manifolds serve as a trampoline to the investigation of the geometry of Poisson manifolds and the different facets of their quantization. This should let us address a number of open questions in Poisson Geometry and the study of its quantization from a brand-new perspective.

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From Symplectic to Poisson manifolds and back

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