AWMA virtual seminar n°12

The speaker, Prof. Aissa Wade is a professor of Mathematics at Penn State University. She was the head of the African Institute of Mathematical Sciences in Senegal during the period 2016-2018. She received her Master’s Degree in Mathematics from the University of Dakar, Senegal and her PhD in Mathematics from University Montpellier 2, France before joining the Abdus Salam International Centre for Theoretical Physics as a Postdoctoral Fellow. She has held visiting positions at several institutions including The University of North Carolina, The African University of Science and Technology and The University Paul Sabatier in Toulouse, France. Her research interests are in Poisson Geometry and related areas such as Symplectic Topology, Contact Geometry, and Mathematical Physics.



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Date Friday  January 14, 2022
Time 14:00-15:00 (UTC)
Speaker Prof Aissa WADE
Affiliation Penn State University
Domain Differential Geometry
Title Modular class of Poisson manifolds and Jacobi boundles

In this talk, we will discuss modular classes of Poisson manifolds and Jacobi bundles. The study of modular classes of Poisson manifolds goes back to Koszul’s work in 1985. The modular class of a Poisson manifold is a class in the first Lichnerowicz-Poisson cohomology group that determines the obstruction to the existence of a volume form, which is invariant under the flows of all Hamiltonian vector fields.
A Jacobi bundle is a line bundle L over a smooth manifold M equipped with a Lie bracket on sections of L, which is a derivation with respect to each of its two entries. This is also known as Kirillov’s local algebra structure. When the line bundle is trivial, one recovers Lichnerowicz's notion of a Jacobi manifold, which encompasses the notion of a Poisson structure. We will explain how to extend Koszul’s construction to Jacobi bundles




Friday, January 14, 2022