Venue

Seminar Room, School of Mathematical Sciences

Speaker

Arpan Kabiraj

Affiliation

Chennai Mathematical Institute

Title

Poisson algebras associated to unoriented curves on surfaces

In 1980s Goldman introduced various Lie algebra structures on the free vector space generated by the free homotopy classes of closed curves in any orientable surface F. Naturally the universal enveloping algebra and the symmetric algebra of these Lie algebras admit a Poisson algebra structure. In this talk I will define and discuss some properties of these Poisson algebras. I will briefly explain their connections with symplectic structure of moduli space and the skein algebras of $F\times [0,1]$. This is an ongoing work with Prof. Moira Chas.