Workshop on Resurgence, wall-crossing and geometry

Contribution List

1. From the Kronecker quiver to a Painleve III tau function

Tom Bridgeland

13/01/2025, 09:30

I will explain how to relate the two objects in the title. Along the way we will encounter stability conditions, Donaldson-Thomas invariants, Riemann-Hilbert problems, Joyce structures and isomonodromic deformations. This is joint work with Fabrizio Del Monte.

2. Summability for state integrals of hyperbolic knots

Veronica Fantini

13/01/2025, 11:00

Given a hyperbolic knot K, state integrals are convergent integrals of products of Faddeev’s quantum dilogarithm associated with certain triangulations of S^3\K. Their asymptotic expansions are divergent power series conjectured to be resurgent and Borel summable by Garoufalidis, Gu and Mariño. In this talk, I will prove this conjecture for the knots 4_1 and 5_2. This is based on a joint...

3. Refined Gromov-Witten invariants

Andrea Brini

13/01/2025, 16:30

I will discuss a conjectural definition of refined curve counting invariants of local Calabi--Yau threefolds in terms of equivariant stable maps on Calabi--Yau fivefolds. The corresponding disconnected generating function should conjecturally equate the Nekrasov--Okounkov K-theoretic membrane index under a refined version of the GW/PT correspondence. Physically, this provides a worldsheet...

4. Analytic continuation of topological strings

Murad Alim

13/01/2025, 18:00

The partition function of topological string theory on any family of Calabi-Yau threefolds is defined perturbatively as an asymptotic series in the topological string coupling and encodes, in a holomorphic limit, higher genus Gromov-Witten as well as Gopakumar-Vafa invariants. I will prove that the partition function of topological strings of any CY in this limit can be written as a product,...

5. Periods and the meromorphic 3d index

Stavros Garoufalidis

14/01/2025, 09:30

6. Wall-crossings in Painlevé equatons

Kohei Iwaki

14/01/2025, 11:00

The series of works by Gaiotto, Moore, and Neitzke demonstrated a deep connection between the wall-crossing phenomena of BPS invariants and the Stokes phenomena in exact WKB analysis. In this talk, I will propose an interpretation of the wall-crossing formulas through the analysis of Painlevé equations. Part of this talk is based on joint work with M. Mariño (SIGMA, 2024).

8. European Research Council (ERC) information session

Joan Vazquez Molina

14/01/2025, 18:00

The European Research Council’s mission is to encourage the highest quality research in Europe through competitive funding and to support investigator-driven frontier research across all fields, based on scientific excellence. I will give an overview of the ERC programme and its funding opportunities, open to researchers of any nationality and age. The session will provide insights into the...

9. A guided tour of BPS sectors in 5d, 3d and 3d-5d systems from the viewpoint of exponential networks

Pietro Longhi

15/01/2025, 18:00

BPS states associated to different kinds of resurgent structures, such as Riemann-Hilbert problems for Donaldson-Thomas theory, exact WKB analysis, and knot theory, share deep connections through string theory. In this talk I will review how interactions among these BPS sectors, and related mathematical structures, can be studied through exponential networks

10. Integral Representations of Quantum Invariants of Three-Manifolds

William Mistegard

16/01/2025, 09:30

In this talk we focus on finite dimensional integral representations of topological invariants of three-manifolds which are motivated by resurgence.

Our first example will be the Witten-Reshetikhin-Turaev (WRT) quantum invariant of a three-manifold with a colored link. Our corresponding integral representation, which is joint with Andersen and Hindson, is motivated by Witten's works on...

11. Studying the Borel plane of one-parameter Calabi-Yau models

Amir Kashani-Poor

16/01/2025, 11:00

The topological string amplitude on hypergeometric Calabi-Yau threefolds is known to sufficiently high genus to permit a resurgence analysis, In this talk, based on joint work with Simon Douaud, we study the position of Borel singularities and the associated Stokes constants for these geometries. We find in particular that in models which exhibit massless D-branes at a singular point, the...

12. A categorification of Stokes coefficients in Chern-Simons theory on plumbed 3-manifolds

Pavel Putrov

16/01/2025, 16:30

The Stokes coefficients of the perturbative expansions in Chern-Simons theory around flat connections on a 3-manifold are known to be integers. In my talk, I will describe a way to promote those integers to Z/2-graded vector spaces for a certain large class of non-hyperbolic 3-manifolds. The vector spaces are given by a version of Lagrangian Floer homology in a finite-dimensional space, with...

13. BPS algebras: overview and recent progress

Wei Li

16/01/2025, 18:00

14. Energy Trans-series of Hofstadter Butterfly from Supersymmetric Field Theory

Jie Gu

17/01/2025, 09:30

Electron in a 2d square lattice immersed in a perpendicular magnetic field is known to exhibit a fractal energy spectrum known as the Hofstadter Butterfly. To account for this interesting energy spectrum nonperturbative corrections must be taken into account. We capitalise on an interesting connection between Hofstadter butterfly and 5d supersymmetry field theory, and by making use of the...

15. Spectral networks and spectral determinants

Lotte Hollands

17/01/2025, 11:00

Spectral networks encode an awful lot of information about four-dimensional N=2 theories of class S, but are also an incredibly useful tool to study spectral problems that come up in this context. In this talk I will explain how to analyse spectral problems from the perspective of spectral networks, and how to formulate spectral determinants in terms of spectral coordinates. Parallel to Tom...

7. Integral Representations of Quantum Invariants of Three-Manifolds

William Mistegard

In this talk we focus on finite dimensional integral representations of topological invariants of three-manifolds which are motivated by resurgence.

Our first example will be the Witten-Reshetikhin-Turaev (WRT) quantum invariant of a three-manifold with a colored link. Our corresponding integral representation, which is joint with Andersen and Hindson, is motivated by Witten's works on...