On Quadratic Poisson Structures
Organizers
Speaker
Anton Khoroshkin
Time
Friday, September 26, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
A quadratic Poisson structure is given by a bivector $\pi = \sum \pi_{ij}^{pq} x_p x_q \partial_i \wedge \partial_j$ which satisfies certain compatibility conditions. Forgetting the underlying space with coordinates $x_i$ leads to an algebraic structure known as a (wheeled) properad.
In this talk I will describe several interesting properties of this properad, explain why its deformation theory is as intricate as that of an arbitrary Poisson structure or a Lie bialgebra, and show how the famous Kontsevich graph complex acts on these deformations. I will also emphasize some Gröbner basis techniques to illustrate current methods for algebraic computations with structures such as (pr)operads.
In this talk I will describe several interesting properties of this properad, explain why its deformation theory is as intricate as that of an arbitrary Poisson structure or a Lie bialgebra, and show how the famous Kontsevich graph complex acts on these deformations. I will also emphasize some Gröbner basis techniques to illustrate current methods for algebraic computations with structures such as (pr)operads.