Elliptic Log Symplectic Brackets on Projective Bundles

Mykola Matviichuk, Imperial College London

Poisson brackets are a crucial concept bridging classical mechanics and quantum mechanics. In this talk, I will present a novel approach to constructing holomorphic Poisson brackets that satisfy the log symplectic non-degeneracy condition and have a geometric connection to elliptic curves. This method relies on the deformation theory and involves combinatorics of graphs with decorations. I will demonstrate its effectiveness by creating new examples, as far as my knowledge extends, on complex projective bundles over a polydisc. Additionally, I will revisit and rediscover the Feigin-Odesski log symplectic brackets on projective spaces.

QNC 2501