Workshop in Geometry and Mathematical Physics

May 25, 2026, 9:00 AM → May 26, 2026, 3:00 PM Europe/Rome

7th floow (SISSA)

This is a 2-day workshop that includes the award of the Dubrovin medal.

The winners are 

Elba Garcia-Failde (Universitat Politècnica de Catalunya and Institut de Math'ematiques de Jussieu, Sorbonne Universit´e)

Yang Li (University of Cambridge)

 

Speakers

Gaetan Borot       (Humboldt University,  Berlin)

Marco Bertola     (Concordia University, Montreal)

Guido Carlet        (IMB,  Dijon)

Marta Mazzocco  (ICREAs Barcelona)

Paolo Rossi   (University of Padua)

Giulio Ruzza  (University of Lisbon)

 

 

 

 

 

Mon, May 25

9:15 AM → 10:00 AM MARTA MAZZOCCO TBA

10:00 AM → 10:45 AM GUIDO CARLET, TBA

10:45 AM → 11:15 AM Coffe break

11:15 AM → 12:00 PM PAOLO ROSSI, TBA

2:00 PM → 2:45 PM GAETAN BOROT, Gaussian fluctuations in random lozenge tilings and the Kenyon-Okounkov conjecture

I will describe results for the macroscopic asymptotics in random lozenge tilings in a large class of two-dimensional domains, in particular identifying Gaussian free field fluctuations for the height field. The results rely on an analysis on a discrete Coulomb gas extending the one known for invariant ensembles of random matrices.
This is based on the joint work https://arxiv.org/abs/2601.16377 with Vadim Gorin and Alice Guionnet

2:45 PM → 3:30 PM GIULIO RUZZA Multiplicative statistics of Poissonized Plancherel random partitions

After reviewing the Plancherel measure on partitions and its relevance in combinatorics and (asymptotic) representation theory, I will introduce a class of multiplicative statistics of Poissonized Plancherel random partitions. Their study is motivated by connections to integrable systems (Toda equations) and to important stochastic growth models (polynuclear growth models).
In particular, with Mattia Cafasso and Matteo Mucciconi we tackled the asymptotic study of these statistics. Building on the log-gas structure of the Poissonized Plancherel measure we derived optimal shapes for Poissonized Plancherel random partitions (which generalize the celebrated Vershik-Kerov-Logan-Shepp density and exhibit new behaviors naturally described in terms of elliptic functions) as well as refined asymptotic expansions for the statistics themselves.

3:30 PM → 4:00 PM Coffe break

4:00 PM → 4:45 PM MARCO BERTOLA, TBA

Tue, May 26

10:00 AM → 10:10 AM DIRECTOR PRESENTATION

10:10 AM → 10:20 AM MEDIALAB and LMP presentation

10:20 AM → 11:20 AM Elba Garcia-Failde, Whispers of Topological Recursions: The negative Witten conjecture and a universal duality

opological recursion (TR) is a universal procedure that helps connect diverse areas of mathematics and physics. Starting from a spectral curve—a Riemann surface equipped with additional data—it produces a family of differentials that often encode enumerative invariants, such as volumes of moduli spaces, matrix model correlators, and intersection numbers. After a brief introduction, we explore two stories, in principle unrelated to, yet guided by, TR—almost in a whisper—towards their resolution:
Witten conjectured that the generating series of psi-class intersection numbers is a tau function of the KdV hierarchy, a result first proved by Kontsevich. Norbury later conjectured an analogous statement for intersection numbers of psi-classes times a negative square root of the canonical bundle. We prove Norbury’s conjecture and derive polynomial relations among kappa-classes. We further introduce a new cohomological field theory (CohFT): the negative analogue of Witten’s r-spin CohFT. We show that its intersection numbers are recursively computable via W-constraints and obtain new tautological relations on the moduli space of curves.
The generating series of maps—graphs embedded on surfaces—obeys TR. Exchanging the roles of x and y in the initial data of TR transforms these maps into fully simple maps. Ordinary and fully simple maps are related via monotone Hurwitz numbers, unveiling a universal duality. This duality translates into functional relations between moments and free cumulants, resolving an open problem in free probability that generalises Voiculescu’s R-transform. In this way, we uncover a general theory of freeness which takes into account higher genus corrections and captures the full, all-order asymptotic behaviour of random matrices.

11:20 AM → 12:20 PM Yang Li, Metric SYZ conjecture

The Strominger-Yau-Zaslow conjecture asks for a special Lagrangian fibration on the generic region of a Calabi-Yau manifold close to the large complex structure limit. I will give a survey talk for the recent progress on this question.