Geometry Seminar

University of Tor Vergata, Department of Mathematics

4th of October 2022, 14:30-15:30, room “Dal Passo”

Speaker

Davide Cesare Veniani 

(University of Stuttgartt)

Title

Symplectic rigidity of O'Grady's manifolds

Abstract

Mukai classified all symplectic groups of automorphisms of K3 surfaces as possible subgroups of one of the Mathieu groups. Since then, the proof of Mukai's theorem has been simplified using lattice theoretical techniques, and extended to higher dimensional hyperkähler manifolds. In two joint works with L. Giovenzana (Loughborough), A. Grossi (Chemnitz) et C. Onorati (Roma Tor Vergata), we studied possible cohomological actions of symplectic automorphisms of finite order on the two sporadic deformation types found by O'Grady in dimension 6 and 10. In particular, we showed that, in dimension 10, all symplectic automorphisms are trivial. In my talk, I will explain the connection between our proof and the sphere packing problem, which was recently solved by Fields medalist Viazovska in dimension 8 and 24.