Archives for December 2019

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.