Kick-off event: AI and the future of mathematics and physics - 21.10.2026
In light of recent developments, the incoming kick-off event at the Institut Henri Poincaré will take the form of a debate gathering mathematicians and theoretical physicists around the role of AI in the practice of research. More information will come soon.
Differential equations for the series of hypermaps with control on their full degree profile
byHoucine Ben Dali
Abstract:We consider generating series of hypermaps with controlled degrees of vertices, hyperedges and faces. It is well known that under some particular specializations, these series satisfy the celebrated KP equations in the orientable case, and BKP equations in the non-orientable one. In this talk, I present a family of differential equations which characterizes the full generating series of hypermaps.
I will give a first proof which works for a one parameter deformation of the series of hypermaps related to Jack polynomials. This proof is based on a differential formula for Jack characters obtained in a joint work with Maciej Dołęga. I will also present a combinatorial proof for the orientable case.