Itzykson Seminary
Set up in 2012 at the initiative of LabEx Mathématique Hadamard (LMH), the Itzykson seminar has become the flagship event of the "Mathematics and Theoretical Physics" program (formerly of LMH and now of FMJH), which supports it. It is currently coordinated by Jean-René Chazottes (CPHT), Guillaume Dubach (CMLS), Ruben Minasian (IPhT) and Julio Parra-Martinez (IHES). Each of the seminar sessions takes place at IHES.
Each session lasts a day. The morning is devoted to a preparatory minicourse aimed at understanding how the mathematical formulation of the physical problem was put into place, as well as providing an overview of the issues and history of the subject. The afternoon is devoted to two lectures, typically one given by a mathematician and the other by a physicist.
The topics which have been treated in the colloquium : Quantum Chaos, Planar maps and quantum gravity, Wall crossing in Hitchin integrable systems, Moduli spaces and quantum curves, Feynman Integrals, Out-of-equilibrium statistical physics, Resurgence and quantization, Parafermionic observables and 2D statistical physics, Computational and information-theoretic phase transitions in large-scale inference problems. Some of the sessions are available on dailymotion and youtube.
Among the topics we would like to cover in the future: AdS-CFT correspondence, Cosmology, Black holes, Gauge theories and integrability, bootstrap methods in CFT, Quantum information theory..
The purpose of this seminar is to lay the foundations of a real scientific community around mathematics and fundamental physics in the Saclay / Orsay / Bures region, in particular to share with mathematicians the challenges of contemporary physics. The target audience is mathematicians and physicists, including master's or doctoral students, and postdoctoral fellows.
For practical information, please contact: contact@fondation-hadamard.fr.
14th Itzykson Seminar
Tuesday 1rst December 2026
At Institut des Hautes Études Scientifiques (IHES)
Bures sur Yvette
Details and registration to follow
Intervenants
Cristian Giardinà
From Markov Duality to Discrete Macroscopic Fluctuation Theory
Building on the Lie-algebraic approach to duality, I will revisit the harmonic process and show that it arises as the Markov process associated with the integrable XXX_s Hamiltonian with non-compact spins. Its large-spin limit yields a lattice formulation of macroscopic fluctuation theory whose large-deviation Hamiltonian is the classical Ishimori chain. Exploiting this integrable structure, we solve the current large-deviation problem on the infinite line with step initial data (joint work with K. Mallick, H. Suda, and T. Sasamoto).
Noemi Kurt
Applications of duality: Forward and backward processes in mathematical population genetics
In this talk we will put the main focus on applications of the concept of duality to quite concrete stochastic models. In particular, we will shift focus from the abstract duality framework on the level of generators to consider stochastic processes in a pathwise set up. We will discuss how dual processes may often be interpreted in a strong pathwise sense as forward- and backward pictures of the same underlying stochastic models. This is particularly evident in many classical models of population genetics, such as the Wright-Fisher model, where one process describes the forward evolution of an allele frequency, and the dual process its genealogy. Thanks to this connection, duality may be applied to easily calculate quantities of interest such as fixation probabilities, as we will demonstrate.
We will discuss several such applications in classical population genetics and in population models with dormancy, as well as in interacting particle systems, and discuss connections between strong pathwise dualities and generator dualities.
Frank Redig
Basics and applications of the Lie algebraic approach to Markov duality
Duality is a powerful tool in the study of large-scale stochastic systems (interacting particle systems). These interacting particle systems are used to model phenomena in non-equilibrium statistical physics, as well as in mathematical population genetics. Duality allows to relate complicated interacting systems to simpler systems, e.g. systems with only a few particles, or systems where non-equilibrium driving has been replaced by absorbing boundaries.
In the last decade, a lot of work has been done to relate duality of Markov processes to symmetries of the underlying Markov generator, and from there one is naturally lead towards simple objects in Lie representation theory such as the Casimir, coproduct, tensor products, which become tools to constructively find processes with useful dualities. For symmetric processes (detailed balance setting) these Lie algebras are classical ones (such as SU(2), SU(1,1), SU(n), SU(n,n)), whereas for the corresponding asymmetric processes, their quantum deformations are used.
In this seminar, starting with simple examples, we show how the Lie-algebraic approach allows to unify several processes, and provides a systematic method to produce processes which have some degree of exact solvability. We start with the classical processes such as independent random walkers and the symmetric inclusion process. We will also discuss recent developments in the representation of non-equilibrium states as mixtures of product measures, and how this can be used to study fluctuations of the density profile for such systems.