Our next Math Colloquium will feature Professor Alexander Veselov from Loughborough University and will take place on Friday 6th December from 3:30pm to 4:30pm in the Nash Lecture Theatre (K2.31). The session will be followed by a reception in King's Building K0.19. Hope to see you there!

 

Differential algebra of polytopes and inversion formulas

There is a remarkable relation between Lagrange inversion problem for formal series and combinatorics of Stasheff polytopes, also known as associahedra (Loday, 2005). Analogous link exists for the multiplicative inverse of the power series and special polytopes known as permutohedra.

I will explain how to prove these facts using the differential algebra of polytopes, following joint work with V.M. Buchstaber. I will also discuss the link with the integrable PDEs and Deligne-Mumford moduli spaces in relation with the works of Witten, Kapranov, Getzler and McMullen.

 

About the Speaker:

Professor Alexander Vesselov completed his PhD at Moscow State University, then worked at Landau Institute, Moscow State University, and is now a professor at Loughborough University, where he is Head of the Geometry and Mathematical Physics group. His research focuses on applying algebraic geometry and mathematical physics to explore integrable systems, with particular interest in quantum systems, spectral theory, discrete integrable systems, and Hamiltonian formalism in geometry and topology.