Louis Merlin (Université du Luxembourg) will speak in the geometry seminar on Tuesday 3 March 2020 at 11ham in the Salle des Profs. Louis’ title and abstract are to be announced.

Marvin Dippell (University of Würzburg) will speak in the geometry seminar on Tuesday 21 January 2020 at 11ham in the Salle des Profs. Marvin’s title is Deformation of Coisotropic Algebras and his abstract is below.

Symmetry reduction is one of the key concepts in classical as well as quantum physics. Geometrically, this can be understood as Marsden-Weinstein reduction on symplectic manifolds or, more generally, in the case of a Poisson manifold, as reduction of a coisotropic submanifold. In this talk I will present an algebraic generalization of coisotropic reduction, which also encompasses various quantum reduction schemes. Following ideas from deformation quantization we will discuss deformations of such coisotropic algebras. Obstructions to such deformations will then be understood as cohomology classes in a suitably defined coisotropic Hochschild cohomology.

Mario Garcia-Fernandez (ICMAT, Madrid) will speak in the geometry seminar on Tuesday 24 March 2020 at 11ham in the Salle des Profs. Mario’s title is Gravitating vortices with positive curvature and his abstract is below.

I will overview recent work with Chengjian Yao and Vamsi Pingali in arXiv:1911.09616, where we give a complete solution to the existence problem for gravitating vortices with positive topological constant c>0, as introduced in arXiv:1510.03810. Our main result establishes the existence of solutions provided that a GIT stability condition for an effective divisor on the Riemann sphere is satisfied. To this end, we use a continuity path starting from Yang’s solution with c=0, and deform the coupling constant α towards 0. A salient feature of our argument is a new bound S(g) \geq c for the curvature of gravitating vortices, which we apply to construct a limiting solution along the path via Cheeger-Gromov theory.

Sobhan Seyfaddini (Université Paris Diderot) will speak in the geometry seminar on Tuesday 26 November 2019 at 11h15am in the Salle de Profs. Sobhan’s title is Barcodes and Hamiltonian homeomorphisms and his abstract is below.

Hamiltonian homeomorphisms are those homeomorphisms of a symplectic manifold which can be written as uniform limits of Hamiltonian diffeomorphisms. One difficulty in studying Hamiltonian homeomorphisms (particularly in dimensions greater than two) has been that we possess fewer tools for studying them. For example, (filtered) Floer homology, which has been a very effective tool for studying Hamiltonian diffeomorphisms, is not well-defined for homeomorphisms. We will show in this talk that using barcodes and persistence homology one can indirectly define (filtered) Floer homology for Hamiltonian homeomorphisms. This talk is based on joint projects with Buhovsky-Humiliére and Le Roux-Viterbo.