Seminar: 15th Geometry and Physics

  • Date: –16:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å80101
  • Lecturer: Joerg Teschner (Hamburg U. & DESY), Yan Soibelman (Kansas State University)
  • Contact person: Tobias Ekholm, Maxim Zabzine
  • Seminarium

1. A generalisation of the AGT-correspondence for non-Lagrangian class S theories: An interesting family of non-Lagrangian four-dimensional N=2, d=4 supersymmetric quantum field theories called T_N-theories is predited by string theory. The geometric engineering of these theories gives a prediction for the partition functions of these theories by topological vertex methods. Joint work in progress with I. Coman-Lohi and Elli Pomoni will clarify the relation of these partition function to conformal blocks in Toda CFT, and to the quantisation of moduli spaces of flat SL(N) connections on the three-punctured sphere.

2. Conventional Riemann-Hilbert correspondence relates differential equations and constructible sheaves: Conventional Riemann-Hilbert correspondence relates differential equations and constructible sheaves. We propose to replace the latter by an appropriate Fukaya category. Based on this idea one can study the RH-correspondence not only for differential but also for q-difference and elliptic difference equations. Arising categories can be described, at least in dimension one, in different ways, e.g. in terms of constructible sheaves on ``skeleta" which are not necessarily Lagrangian. If time permits I am going to discuss the corresponding "non-abelian Hodge theory" and its relationship to periodic monopoles.