Summer School of the CRC 1624: Higher structures, moduli spaces and integrability

Abstracts

7. talk 1: Analytic Langlands correspondence

Pavel Etingof (Massachusetts Institute of Technology)

24/08/2026, 10:00

Analytic Langlands correspondence

Let $G$ is a connected reductive group and $X$ a smooth irreducible projective curve, both defined over a field $F$. The goal of the global Langlands program over function fields is to do harmonic analysis on the moduli space (stack) ${\rm Bun}_G(X)$ of principal $G$-bundles on $X$, for various fields $F$. This means that we want to find the spectral decomposition for a family of commuting...

4. talk 2: Categorical structure of Coulomb branches

Sabin Cautis (The University of British Columbia)

24/08/2026, 11:30

Categorical structure of Coulomb branches

Coulomb branches are certain moduli spaces arising in supersymmetric field theory. They include as special cases many spaces of independent interest in geometry and representation theory. In the four-dimensional case, their coordinate rings can be categorified (lifted) to tensor categories that carry a lot of structure. In these talks we will define and explore the structure of such...

8. talk 4: Analytic Langlands correspondence

Pavel Etingof (Massachusetts Institute of Technology)

24/08/2026, 16:00

Analytic Langlands correspondence

9. talk 5: Analytic Langlands correspondence

Pavel Etingof (Massachusetts Institute of Technology)

25/08/2026, 10:00

Analytic Langlands correspondence

12. talk 6: Categorical structure of Coulomb branches

Sabin Cautis (The University of British Columbia)

25/08/2026, 11:30

Categorical structure of Coulomb branches

10. talk 7: Analytic Langlands correspondence

Pavel Etingof (Massachusetts Institute of Technology)

25/08/2026, 14:30

Analytic Langlands correspondence

11. talk 9: Analytic Langlands correspondence

Pavel Etingof (Massachusetts Institute of Technology)

26/08/2026, 10:00

Analytic Langlands correspondence

13. talk 10: Categorical structure of Coulomb branches

Sabin Cautis (The University of British Columbia)

26/08/2026, 11:30

Categorical structure of Coulomb branches

14. talk 14: Categorical structure of Coulomb branches

Sabin Cautis (The University of British Columbia)

27/08/2026, 11:30

Categorical structure of Coulomb branches

Coulomb branches are certain moduli spaces arising in supersymmetric field theory. They include as special cases many spaces of independent interest in geometry and representation theory. In the four-dimensional case, their coordinate rings can be categorified (lifted) to tensor categories that carry a lot of structure. In these talks we will define and explore the structure of such...

1. Higher groupoids and generalized Kähler geometry

Marco Gualtieri (University of Toronto, UPC in Barcelona)

The traditional description of the 2-dimensional sigma model with N=(2,2) supersymmetry involves a target geometry known as a generalized Kähler metric. Recently, we have understood that this description is only infinitesimal in nature, and that a full description of the model requires the specification of analogues of principal bundles in the form of holomorphic symplectic 2-groupoid...

3. Methods for BPS state counting in type II strings on Calabi-Yau threefolds

Boris Pioline (Laboratoire de Physique Théorique et Hautes Energies)

Four-dimensional string vacua and quantum field theories with $N=2$ supersymmetry exhibit a rich spectrum of supersymmetric bound states, which depends sensitively on the values of the moduli fields or gauge theory parameters. In the context of type II string theories compactified on a Calabi-Yau threefold, the index counting these states coincides with the Donaldon-Thomas invariants...

2. Stablility and PDEs in mirror symmetry

Tristan Collins (University of Toronto)

This lecture series will introduce the special Lagrangian and deformed Hermitian-Yang Mills equation, nonlinear geometric PDEs arising in the context of mirror symmetry. The expectation as that the solvability of these equations is related to algebro-geometric notions of stability. We will explain some historical developments motivating this picture and discuss some more recent progress.