Abstracts of the talks of the Seminar "Colmar" Wintersemester 21/22

â€‹

â€‹

Nicholas Lindsay (U. of Cologne), "Hamiltonian S^1 actions on complete intersections", 21.10.21

â€‹

Abstract:

In this talk I will discuss Hamiltonian circle actions on closed symplectic manifolds. Jones and Ranwsley proved that if the fixed point set is isolated then the signature of the manifold may be expressed as the alternating sum of the even Betti numbers of the manifold.

Inspired by a result of Dessai and Wiemeler which classified smooth circle actions on 6-dimensional complete intersections, I study Hamiltonian circle actions on higher dimensional complete intersections using a generalised version of Jones and Rawnsley’s formula.

â€‹

â€‹

â€‹

Anton Ayzenberg (HSE University), "Face posets of equivariantly formal torus actions", 17.11.21

â€‹

Abstract:

Consider a smooth torus action on a connected closed manifold X of real dimension 2n such that the fixed point set is finite and nonempty. The action is called equivariantly formal if odd degree cohomology of X vanishes. For example, hamiltonian actions on compact manifolds with isolated fixed points are equivariantly formal.

Connected components of X^G, for some subgroup G of T, are called face submanifolds of X. We study the graded poset of face submanifolds both in general and in particular interesting examples. For general equivariantly formal actions we prove certain acyclicity properties of face posets generalizing cohen-macaulayness of toric varieties. If time allows, I show some particular examples of torus actions, whose face posets are graphicahedra - a certain nonconvex generalization of a permutohedron.

The talk is based on several works (as well as works in progress) with Mikiya Masuda, Grigory Solomadin, and Victor Buchstaber.

â€‹

â€‹

Lisa Jeffrey (University of Toronto), "Poisson maps between character varieties: gluing and capping", 16.12.21

â€‹

Abstract:

In this talk I describe mappings between character varieties induced by mappings between surfaces. I will show that these mappings are generally Poisson.

(Joint with Indranil Biswas, Jacques Hurtubise and Sean Lawton,

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹

â€‹