The borderline between theoretical physics and mathematics has seen a remarkable progress over the last 20 years, with gauge theory, string theory, 4-manifold topology, Floer homology theories, etc. The seminar aims at increasing the interaction between the two disciplines. Both mathematicians and physicists will speak in the seminar, and the talks will hopefully be understandable by both communities.

The events are jointly organized by the Department of Mathematics and the Department of Physics and Astronomy.

Organizers: Tobias Ekholm and Maxim Zabzine

Sixteenth Uppsala Geometry and Physics Seminar, April 10, 2018

Geometry of Riemann-Hilbert correspondence
Speaker: Yan Soibelman
Department: Kansas State University
Time: 2018-04-10 13:30 – 14:30
Location: Häggsalen, 10132, Ångströmlaboratoriet

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.

Fifteenth Uppsala Geometry and Physics Seminar, December 6, 2017

A generalisation of the AGT-correspondence for non-Lagrangian class S theories
Speaker: Jörg Teschner
Department: Hamburg U & DESY
Time: 2017-12-06 13:30 – 14:30
Location: Å80101, Ångströmlaboratoriet

An interesting family of non-Lagrangian four-dimensional N=2, d=4 supersymmetric quantum field theories called TN-theories is predicted 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.

Lagrangian fibrations on the projective plane and classification
Speaker: Georgios Dimitroglou Rizell
Department: Uppsala University
Time: 2017-12-06 15:00 – 16:00
Location: Å80101, Ångströmlaboratoriet

The mirror of the projective plane in the sense of homological mirror symmetry consists of Landau-Ginzburg models built from Lagrangian torus fibrations on complements of elliptic curves. In ongoing work with T. Ekholm and D. Tonkonog we extend the construction to the case of certain singular torus fibrations. We also discuss recent classification results for Lagrangians in this setting.