Intersections of Topological Recursion, Conformal Field Theory, and Random Geometry

Contribution List

1. Bertrand Eynard

25/08/2025, 09:00

Lectures on Topological recursion and CFT

2. Guillaume Baverez and Remi Rhodes

25/08/2025, 10:45

Probablistic construction of CFT and applications to Virasoro conformal blocks.

We present a probabilistic construction of Liouville Conformal Field Theory (LCFT), starting with Segal’s axioms and the structure constants (the DOZZ formula). Then, we show how to extract the Virasoro algebra from the semigroup of annuli, and use this data in the spectral theory of the Hamiltonian. Finally, we...

7. Vladimir Fock and Alexander Goncharov

25/08/2025, 14:30

Quantization of cluster Poisson varieties and its applications to CFT

The first talk will be an introductory lecture about cluster quantization. In the second talk we plan to cover some more advanced subjects (integration on moduli and recurrence relations using clusters). The third talk concerns Steinberg symbols, vertex operators and clusters.

10. Alba Grassi

25/08/2025, 16:15

On quantum curves and q-deformed isomonodromic equations.

In recent years, a rich interplay has developed between topological string theory, quantum operators associated with mirror curves, and isomonodromic equations together with their q-deformations. In this talk, I will focus on two operators: the well-known modified Mathieu operator and the less familiar but equally intriguing...

11. Shinji Koshida

25/08/2025, 17:30

Tensor categories arising from the Virasoro algebra and quantum groups.

When studying conformal field theory in two dimensions, one naturally encounters primary fields and their operator product expansions. These can be interpreted as simple objects and tensor products in a tensor category.

Two well-known sources of tensor categories are quantum groups and vertex operator algebras...

3. Bertrand Eynard

26/08/2025, 09:00

Lectures on Topological recursion and CFT

5. Guillaume Baverez and Remi Rhodes

26/08/2025, 10:45

Probablistic construction of CFT and applications to Virasoro conformal blocks.

We present a probabilistic construction of Liouville Conformal Field Theory (LCFT), starting with Segal’s axioms and the structure constants (the DOZZ formula). Then, we show how to extract the Virasoro algebra from the semigroup of annuli, and use this data in the spectral theory of the Hamiltonian. Finally, we...

14. Antti Kupiainen

26/08/2025, 18:00

Wess-Zumino-Witten models and path integrals.

The Wess-Zumino-Witten (WZW) model is a 2 dimensional conformal field theory (CFT) where the field takes values in a Lie group G or its coset space. For a compact group G this CFT is rational and its cosets G/H include for instance all unitary rational CFTs (e.g. the two dimensional Ising model). WZW model has a formal path integral...

4. Bertrand Eynard

27/08/2025, 09:00

Lectures on Topological recursion and CFT

6. Guillaume Baverez and Remi Rhodes

27/08/2025, 10:45

Probablistic construction of CFT and applications to Virasoro conformal blocks.

We present a probabilistic construction of Liouville Conformal Field Theory (LCFT), starting with Segal’s axioms and the structure constants (the DOZZ formula). Then, we show how to extract the Virasoro algebra from the semigroup of annuli, and use this data in the spectral theory of the Hamiltonian. Finally, we...

26. Kento Osuga

27/08/2025, 14:30

N = 1 Super Topological Recursion.

A concrete relation between topological recursion and (modules of) the Virasoro algebra is well understood from the perspective of Airy structures. In fact, the notion of Airy structures plays an important role to generalise into the higher-rank setting, i.e. higher-ramified spectral curves and W-algebras of higher rank. Now, an intereseting question is:...

9. Vladimir Fock and Alexander Goncharov

27/08/2025, 16:00

Quantization of cluster Poisson varieties and its applications to CFT

The first talk will be an introductory lecture about cluster quantization. In the second talk we plan to cover some more advanced subjects (integration on moduli and recurrence relations using clusters). The third talk concerns Steinberg symbols, vertex operators and clusters.

8. Vladimir Fock and Alexander Goncharov

27/08/2025, 17:30

Quantization of cluster Poisson varieties and its applications to CFT

The first talk will be an introductory lecture about cluster quantization. In the second talk we plan to cover some more advanced subjects (integration on moduli and recurrence relations using clusters). The third talk concerns Steinberg symbols, vertex operators and clusters.

16. Dalimil Mazac

28/08/2025, 09:00

L-functions, automorphic spectra, and the conformal bootstrap.

Recently, a close parallel emerged between the spectral theory of automorphic forms and conformal field theory in general dimension. I will review this connection and explain how it can be leveraged to prove new results in number theory and spectral geometry using ideas borrowed from the conformal bootstrap. In particular, I...

17. Kohei Iwaki

28/08/2025, 10:30

Topological recursion and irregular conformal block via Painleve and WKB

Abstract: We will compare topological recursion and irregular conformal blocks, focusing on the Painlevé I equation. If time permits, we will also discuss a relation between the Heun accessory parameter with irregular singularities and the Voros periods.

This talk is based on joint work with N. Iorgov, O. Lisovyy,...

18. Leonid Chekhov

28/08/2025, 11:30

Fool’s crowns, Schwarzian, and topological recursion.

For a Riemann surface with holes, we propose a variant of the action on a circumference-P boundary component with n bordered cusps attached (a “fool’s crown”) that is decoration-independent and generates finite volumes V crown of the corresponding moduli spaces when integrated against the volume n,P form obtained by inverting the...

24. Norman Do

28/08/2025, 14:45

The double-scaled SYK model and Weil-Petersson volumes.

Okuyama expressed correlators in the double-scaled SYK model in terms of q-dependent polynomials arising from topological recursion on a particular spectral curve. He claimed that these polynomials recover the Weil-Petersson volumes studied by Mirzakhani in the limit as q approaches 1. In this talk, we discuss one-and-a-bit proofs of...

23. Baptiste Cercle

28/08/2025, 16:15

Boundary Liouville theory: from classical to quantum and back again.

In this talk we will discuss a geometric problem related to boundary Liouville CFT and closely related to uniformisation of open Riemann surfaces. Namely in a first part we will consider the classical problem of finding a conformal metric with constant scalar curvature, piecewise constant geodesic curvature and prescribed...

19. Xin Sun

28/08/2025, 17:30

Three Theorems on the 6j symbol of the modular double of Uq(sl2(R)).

The modular double of Uq(sl2(R)) is an important quantum group in mathematical physics with a continuous spectrum of representations. The 6j symbol from its tensor structure, also known as the Racah-Wigner coe- ficients, were computed explicitly by Ponsot and Teschner. In this talk, I will present three theorems I proved...

20. Promit Ghosal

29/08/2025, 09:00

Semiclassical Limit of Conformal Blocks, Nekrasov--Rosly--Shatashvili Relations, and the Trieste Formula for the Heun Equation.

This talk reviews recent advances in understanding the semiclassical limit of conformal blocks on the torus. Within this framework, we present ongoing work on the Nekrasov--Rosly--Shatashvili relations in gauge theory, their implications for semiclassical Liouville...

21. Baojun Wu

29/08/2025, 10:30

Conformal Bootstrap for boundary Liouville CFT.

In this talk, I will explain how to compute the Liouville correlation function for surfaces with boundary via the conformal bootstrap method. In the first part, I will explain my previous work establishing the integrability of Liouville CFT on the annulus. This result leveraged the known spectral resolution for the bulk Liouville theory and...

22. Open problem and discussion session

29/08/2025, 11:30

25. Antti Kupiainen

15. Baptiste Cercle

Conformal Bootstrap for boundary Liouville CFT.

In this talk we will discuss a geometric problem related to boundary Liouville CFT and closely related to uniformisation of open Riemann surfaces. Namely in a first part we will consider the classical problem of finding a conformal metric with constant scalar curvature, piecewise constant geodesic curvature and prescribed conical singularities...

12. Kento Osuga

N = 1 Super Topological Recursion.

A concrete relation between topological recursion and (modules of) the Virasoro algebra is well understood from the perspective of Airy structures. In fact, the notion of Airy structures plays an important role to generalise into the higher-rank setting, i.e. higher-ramified spectral curves and W-algebras of higher rank. Now, an intereseting question is:...

13. Norman Do