**Geometry and Physics colloquia
**

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 diciplines. 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 Department of Mathematics and Department of Physics and Astronomy.

Organizers: Tobias Ekholm and Maxim Zabzine

Previous events can be found here.

**Seventeenth Uppsala Geometry and Physics Seminar, May 24, 2018**

Bosonization on a lattice in higher dimensions

Speaker: Anton Kapustin

Department: Caltech, USA

Time: 2018-05-24 13:30 – 14:30

Location: Häggsalen, 10132, Ångströmlaboratoriet

I describe a generalization of the Jordan-Wigner transformation for lattice systems of arbitrary dimension. It maps any fermionic system on a D-dimensional lattice to a (D-1)-form Z_2 gauge theory. The map preserves locality of the Hamiltonian.

**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: Joerg 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 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.

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.

**Fourteenth Uppsala Geometry and Physics Seminar, April 20, 2017**

Quantum invariants of singularities and matrix factorizations

Speaker: Arkady Vaintrob

Department: University of Oregon, USA

Time: 2017-04-20 13:30 – 14:30

Location: Häggsalen, Ångströmlaboratoriet

I will discuss a cohomological field theory related to a quasihomogeneous singularity W with a group G of its diagonal symmetries (a Landau-Ginzburg A-model). The state space of this theory is the equivariant Milnor ring of W and its correlators are analogs of the Gromov-Witten invariants for the non-commutative space associated with the pair (W,G). In the case of simple singularities of type A they control the intersection theory on the moduli space of higher spin curves. The construction is based on categories of equivariant matrix factorizations.

Kähler-Einstein metrics emerging from free fermions

Speaker: Robert Berman

Department: Chalmers, Sweden

Time: 2017-04-20 15:00 – 16:00

Location: Häggsalen, Ångströmlaboratoriet

In this talk I will describe a statistical mechanical approach to the construction of Kähler-Einstein metrics on a complex algebraic variety X, i.e. Kähler solutions to Einstein’s vacuum field equations. The microscopic theory is given by a canonical fermion gas on X whose one-particle states are pluricanonical holomorphic sections on X. The convergence problem in the case of a positive cosmological constant (i.e. the case when X is a Fano manifold) is still open and turns out to be closely connected to the Yau-Tian-Donaldson conjecture in Kähler geometry. Some intriguing relations to the AdS/CFT correspondence will also be pointed out.

**Thirteenth Uppsala Geometry and Physics Seminar, January 23, 2017**

Dirac geometry and Poisson homogeneous spaces

Speaker: Henrique Bursztyn

Department: IMPA, Rio de Janeiro

Time: 2017-01-23 13:30 – 14:30

Location: Polhemsalen, Ångströmlaboratoriet

We will give a brief introduction to Dirac structures, which are geometric objects extending Poisson as well as presymplectic structures. They arise naturally as the geometric framework for mechanical systems with constraints, but their recent applications are far reaching, including e.g. generalized complex geometry and the theory of moment maps. In this talk, I will explain how Dirac structures can be used as a tool to solve the problem of integrating Poisson homogeneous spaces.

Teichmüller TQFT and traces of unitary operators

Speaker: Rinat Kashaev

Department: Geneva Univ

Time: 2017-01-23 15:00 – 16:00

Location: Polhemsalen, Ångströmlaboratoriet

The Teichmüller TQFT induces unitary projective representations of punctured surfaces in infinite dimensional Hilbert spaces. The partition functions of the mapping tori of pseudo Anosov elements are finite in this theory provided a version of the volume conjecture for Teichmüller TQFT is satisfied. That means that the traces of the corresponding unitary operators and of all their powers can be defined even if these are not trace class operators.