Previous seminars

Tuesday 11th of June: Gaultier Lambert (KTH) 

 Scaling limits of the Gaussian beta-ensemble characteristic polynomial

Abstract: The Gaussian beta-ensemble or one-dimensional log-gas is a classical model of random matrix theory which describes a gas of electric charges confined on the real line which interact via the two-dimensional Coulomb kernel. I will report on recent asymptotic results for the characteristic polynomial of these ensembles at general inverse-temperature beta. These asymptotics involve the so-called Sine and Airy processes, as well as a Gaussian log-correlated field, and they should be compared to the classical Plancherel-Rotach asymptotics for the Hermite polynomials (β = ∞). The proof are based on the Dumitriu-Edelman tridiagonal representation of the Gaussian beta-ensemble and the transfer matrix method. If time permits, I will also mention some connections to Gaussian multiplicative  chaos. Joint work with Elliot Paquette (McGill University).

Monday 27th of May: Léonie Papon (University of Durham) 

 A level line of the massive Gaussian free field 

Abstract: I will present a coupling between a massive planar Gaussian free field (GFF) and a random curve in which the curve can be interpreted as the level of the field. This coupling is constructed by reweighting the law of the standard GFF-SLE_4 coupling. I will then show that in this coupling, the marginal law of the curve is that of a massive version of SLE_4, called massive SLE_4. This law on curves was introduced by Makarov and Smirnov to describe the scaling limit of a massive version of the harmonic explorer. Time permitting, I will also explain how to reweight the law of the coupling GFF-CLE_4 to obtain a coupling between a massive GFF and a massive version of CLE_4.

Friday 24th of May: Marcello Porta (International School for Advanced Studies)

 Universal edge transport in 2d topological insulators

Abstract: In this talk I will review the application of rigorous renormalization group methods to the study of charge transport in interacting gapless fermionic lattice models, of relevance for condensed matter physics. I will outline a strategy that has been used over the years to compute the response functions of a wide class of systems, and to prove universality. I will focus on the case of edge currents for interacting 2d topological insulators, which fall into the universality class of the multichannel Luttinger model. I will discuss how the RG analysis, combined with lattice and emergent Ward identities, can be used to prove the quantization of the edge conductance, implying in particular the validity of the bulk-edge duality for interacting 2d quantum Hall systems.

Monday 13th of May: Adam Harper (University of Warwick) 

 Large fluctuations of random multiplicative functions

Abstract: Random multiplicative functions $f(n)$ are a well studied random model for deterministic number theoretic functions like Dirichlet characters or the Mobius function. Arguably the first question ever studied about them, by Wintner in 1944, was to obtain almost sure bounds for the largest fluctuations of their partial $\sum_{n \leq x} f(n)$, seeking to emulate the classical Law of the Iterated Logarithm for independent random variables. In this talk I will describe a (fairly) recent result in the direction of sharply determining the size of these fluctuations. I hope to get to some interesting details of the new proof in the latter part of the talk, but most of the discussion should be widely accessible. It turns out that there are significant connections with the notion of (Gaussian) multiplicative chaos, from probability and mathematical physics.

Monday 06th of May: Lucas D’Alimonte (Fribourg) 

Ornstein-Zernike theory for the 2D near-critical random cluster model

Abstract: In this talk, we will discuss the classical Ornstein—Zernike theory for the random-cluster models (also known as FK percolation). In its modern form, it is a very robust theory, which most celebrated output is the computation of the asymptotically polynomial corrections to the pure exponential decay of the two-points correlation function of the random-cluster model in the subcritical regime. We will present an ongoing project that extends this theory to the near-critical regime of the two-dimensional random-cluster model, thus providing a precise understanding of the Ornstein—Zernike asymptotics when p approaches the critical parameter p_c. The output of this work is a formula encompassing both the critical behaviour of the system when looked at a scale negligible with respect to its correlation length, and its subcritical behaviour when looked at a scale way larger than its correlation length.

Based on a joint work with Ioan Manolescu.

Tuesday 30th of April: Frank Ferrari (Université Libre de Bruxelles)

 Jackiw-Teitelboim Gravity, Random Disks of Constant Curvature, Self-Overlapping Curves and Liouville CFT1

Abstract: Jackiw-Teitelboim quantum gravity is a model of two-dimensional gravity for which the bulk curvature is fixed but the extrinsic curvature of the boundaries is free to fluctuate. The negative curvature model has been studied extensively in the recent physics literature, in a particular ``Schwarzian'' limit, because of its relevance in describing quantum black holes and their SYK-like duals.

A first-principle approach reveals that the description used in the literature so far is an effective theory valid on distances much larger than the curvature length scale of the bulk geometry.

At the microscopic level, the theory should be defined by taking the continuum limit of a new model of random polygons. The polygons, called ``self-overlapping,'' are constrained to bound a disk immersed in the plane. They must be counted with an appropriate multiplicity. The solution of the model could be found in principle by solving a difficult ``dually weighted’' Hermitian matrix model.

Motivated by standard heuristic path integral arguments, mimicking similar arguments used for Liouville gravity in the 80s and the 90s, we conjecture that an equivalent description is obtained in terms of a boundary log-correlated field. This yields predictions for the critical exponents of the self-overlapping polygon models and open the path to a wide range of potential applications.

Monday 29th of April: Réka Szabó (University of Groningen) 

Stability results for random monotone cellular automata 

Abstract: In a monotone cellular automaton, each site in the d-dimensional integer lattice can at each integer time take the values zero or one. The value of a site at a given time is a monotone function of the values of the site and finitely many of its neighbours at the previous time. Toom’s stability theorem gives necessary and sufficient conditions for the all one state to be stable under small random perturbations. We review Toom’s Peierls argument and extend it to random cellular automata, in which the functions that determine the value at a given space-time point are random and i.i.d. We are especially interested in the case where with positive probability, the identity map is applied. Being able to include this map is important for understanding continuous-time interacting particle systems that can be seen as limits of discrete-time cellular automata. We derive sufficient conditions for the stability of such random cellular automata. Joint work with Cristina Toninelli and Jan Swart. 

Monday 15th of April: Raphael Ducatez (Université Claude Bernard Lyon 1)

Full large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices

We establish precise estimates for the probability of rare events of the largest eigenvalue of Wigner matrices with sub-Gaussian entries. In contrast to the case of Wigner matrices with heavier tails, where deviations are governed by the appearance of a few large entries, and the sharp sub-Gaussian case that is governed by the collective deviation of entries in a delocalized rank-one pattern, we show that in the general sub-Gaussian case that deviations can be caused by a mixture of localized and delocalized changes in the entries. Our key result is a finite-N approximation for the probability of rare events by an optimization problem involving restricted annealed free energies for a spherical spin glass model. This allows us to derive full large deviation principles for the largest eigenvalue in several cases, including when the law of the matrix entries is compactly supported and symmetric, as well as the case of randomly sparsified GOE matrices. 

Joint work with A. Guionnet and N. Cook.

Monday 8th of April: Christoforos Panagiotis (University of Bath)

Random tangled currents and the continuity of the phase transition for $\phi^4$

In this talk, I will give an overview of my recent work on $\varphi^4$ with Trishen Gunaratnam, Romain Panis and Franco Severo. I will describe the random tangled current representation and discuss how we used it to prove that the phase transition of the $\varphi^4$ model is continuous in dimensions $d\geq 3$, and to characterise the structure of translation invariant Gibbs measures. Along the way, I will mention some open problems and our ongoing work on the supercritical behaviour of $\varphi^4$. 

Monday 25th of March : Alessio Ranallo (Unige)

Low energy spectrum of the XXZ model coupled to a magnetic field. 

I will report on recent developments concerning the control of a class of short-range perturbations of the Hamiltonian of an Ising chain. An example covered by our analysis is the celebrated XXZ chain. This is a joint work with S. Del Vecchio, J. Fröhlich, and A. Pizzo.  

Monday 18th of March : Dominik Schmid (University of Bonn)

Biased random walk on dynamical percolation

We consider a biased random walk on dynamical percolation and discuss the existence and the properties of the linear speed as a function of the bias. In particular, we establish a simple criterion to decide whether the speed is increasing or decreasing for large bias. This talk is based on joint work with Sebastian Andres, Nina Gantert, and Perla Sousi.

Monday 11th of March :  Jean Barbier (International Center for Theoretical Physics)

A multi-scale cavity method, with application to sub-linear rank matrix denoising

The cavity method is a powerful approach from the mathematical physics of spin glasses allowing to rigorously tackle the computation of log-partition functions and order parameters in mean-field spin models. I will present a generalization which allows to treat models where the variables are not simple finite-dimensional spins but are instead matrices whose dimensions M,N both grow in the thermodynamic limit; this in contrast with standard spin models where only one parameter, the number N of variables in the system, grows large. I will present the method in the context of an inference problem known as matrix denoising, in the challenging regime where the matrix to infer has a rank M (slowly) growing with its size N.

Monday 04th of March :  Benoît Laslier (Université de Paris)

Tilted Solid on Solid is liquid, at least if thawed a bit. 

The (2+1)D SOS model is a famous example of an effective interface model designed to approximate the boundary between two law temperature phases in 3D Ising. In the classical setting with 0 boundary condition, it exhibits a roughening transition where the variance of the height stays bounded at large beta while it diverges logarithmically with the size of the domain at small beta. However, not all surfaces can be aligned with the underlying lattice, so what happens in presence of a slope ?

For a class of SOS type surface, we show that any slope destabilize the rigidity of the 0 boundary condition and that for beta large enough the fluctuations of the interface converge to a Gaussian free field. To our knowledge, this is the first example in any tilted so called "grad phi" model or perturbation of one where the scaling limit has been obtained. The proof goes though an approximation of the SOS surface by a monotone surface and establishes first that the resulting law is a form of weakly interacting dimer model and second that the renormalization tools of Giuliani-Mastropietro-Toninelli (2017) apply to it, leading to the scaling limit. 

Monday 26th of February : François Pagano (Geneva)

Localization and eigenfunctions to 2nd - order elliptic PDEs

In the 70’s, Anderson studied the motion of electrons in materials. If the atomic structure is periodic, electrons can travel freely: the material conducts electricity. On the other hand, if the material has impurities or if the atomic structure is more random, electrons can get trapped: the material is now an insulator. Anderson received the Nobel Prize in Physics for this discovery in ’77.

Understanding this question mathematically amounts to understanding the nature of the spectrum for a periodic or random Schrödinger operator. 

In this talk, we will first illustrate, using results from Kuchment (’12) and Bourgain-Kenig (’05), how this problem is related to the following (deterministic) question going back to Landis (late 60' s): given A elliptic, C^1 (or smoother) and V bounded, how rapidly can a non-trivial solution to −div(A∇u) + V u = 0 decay to zero at infinity?

 We will discuss the construction of an operator on the cylinder T^2 × R with an eigenfunction div(A∇u) = −µu, which has double exponential decay at both ± ∞, where A is uniformly elliptic and uniformly C^1 smooth in the cylinder.

Joint work with S. Krymskii and A. Logunov.

Monday 18th of December : Antoine Jego (EPFL)

Thick points of 4d critical branching Brownian motion

I will describe a recent work in which we prove that branching Brownian motion in dimension four is governed by a nontrivial multifractal geometry and compute the associated exponents. As a part of this, we establish very precise estimates on the probability that a ball is hit by an unusually large number of particles, sharpening earlier works by Angel, Hutchcroft, and Jarai (2020) and Asselah and Schapira (2022) and allowing us to compute the Hausdorff dimension of the set of “a-thick” points for each a > 0. Surprisingly, we find that the exponent for the probability of a unit ball to be “a-thick” has a phase transition where it is differentiable but not twice differentiable at a = 2, while the dimension of the set of thick points is positive until a = 4. If time permits, I will also discuss a new strong coupling theorem for branching random walk that allows us to prove analogues of some of our results in the discrete case. 

Monday 11th of December : Yilin Wang (IHÉS)

Conformal restriction and Onsager-Machlup functional for SLE loop measure

Onsager-Machlup functional measures how likely a stochastic process stays close to a given path. SLE is a family of measures on simple paths in the plane introduced by O.Schramm obtained from the Loewner transform of a multiple of Brownian motion. We show that the Onsager-Machlup of the SLE_k loop measure, for any 0 < k \le 4, is expressed using the Loewner energy and the central charge c(k) of SLE_k. The proof relies on the conformal restriction covariance of SLE and an observation relating two ways to renormalize the Brownian loop measure. This is based on the joint work (arXiv: 2311.00209) with Marco Carfagnini (UCSD). If time permits, I will show one application of this result, which gives a representation of the Virasoro algebra using SLE loop measure. (This is work in progress with Masha Gordina and Wei Qian).

Monday 04th of December : Nikolai Kuchumov (LPSM)

Variations and harmony in the domino world

The talk will consist of two parts. The first half is based on the work arXiv:2110.06896, we will discuss random domino tilings of multiply connected domains: the classical Arctic circle theorem, and its extension to a multiply connected domain with a help of a variational principle, where the height function obtains a monodromy, non-zero increment going around a loop. 

In the second half, we will focus on the new method of computation of the frozen curve, which generalize the Arctic circle, and the main tool will be the tangent plane method proposed by Rick Kenyon and Istvan Prause in 2020 in arXiv:2006.01219. If time permits, we will also discuss work in progress with this method for a multiply connected Aztec diamond.

Monday 27th of November : Hugo Vanneuville (Grenoble)

A new proof of exponential decay in Bernoulli percolation

Bernoulli percolation of parameter p on Z^d is defined by deleting each edge of Z^d with probability 1-p, independently of the other edges. The exponential decay theorem (for the volume) is the following result (proven in the 80's): If the volume of the cluster of 0 is a.s. finite at some parameter p, then it has an exponential moment at any parameter q<p. I like to state this theorem this way because it illustrates the fact that "decreasing p infinitesimally has a regularising effect on the percolating clusters". The goal of this talk is to propose a new proof of this theorem, inspired by Russo's work from the early 80s, which proposes to show that conditioning on a well-chosen decreasing event has less effect than decreasing p a little.

Monday 20th of November : Salvador Cesar Esquivel Calzada (Muenster)

  A priori bounds for subcritical fractional Phi^4 on the torus

 In this talk I will present a new result on a priori bounds for the dynamical Phi4 model in fractional dimensions covering the full sub-critical regime using fractional powers of the Laplacian. This model arises as the stochastic quantization of the Brydges-Mitter-Scoppola model in EQFT.

Monday 13th of November : Chiranjib Mukherjee (Muenster)

  Percolation and geometry of groups 

We will use group-invariant percolation on Cayley graphs of finitely generated groups to study its geometric properties. In particular, it will be shown such a group has the so-called  Haagerup property if and only if for any $\alpha\in (0,1)$, there is a group- invariant bond percolation whose marginals exceed $\alpha$ and whose two-point function vanishes at infinity. Our result is inspired by the characterization of amenability by Benjamini, Lyons, Peres and Schramm. A key idea is to use the characterization of the Haagerup property in terms of actions on spaces with measured walls in the sense of Cherix, Martin and Valette and the proof is based a new construction using invariant point processes on such spaces with measured walls, which leads to quantitative bounds on the two-point functions. Moreover, the method allows us to strengthen a consequence of Kazhdan's property (T), due to Lyons and Schramm, to an equivalence in terms of the marginals and the two-point point function. These results are then used to give a new proof of the fact, already observed by Gaboriau and Tucker-Drob, that there is no unique infinite cluster at the uniqueness threshold for Bernoulli bond percolation on Cayley graphs of groups admitting an infinite normal subgroup with relative property (T). 

Monday 6th of November : Remi Rhodes (Aix-Marseille)

  Coulomb gas and compactified imaginary Liouville theory

Conformal Field Theories (CFT) play a central role in the description of statistical physics models undergoing a second order phase transition at their critical point. The recent development of the Liouville CFT, which is the scaling limit of random planar maps, has shed some light on the mathematical structure of CFT and has had many applications regarding the derivation of exact formulae for various statistical physics models. In this talk I will present the probabilistic  construction of another important CFT, called imaginary Liouville CFT, and explain why it satisfies the axioms of CFT, in particular Segal’s gluing axioms. In physics this path integral is conjectured to describe the scaling limit of critical loop models such as Q-Potts or O(n) models. This CFT has several exotic features: most importantly, it is non unitary and has the structure of a  logarithmic CFT. Therefore it provides a playground for the mathematical study of these concepts.

Monday 30th of October : Eleanor Archer (Paris Nanterre)

  Scaling limit of high-dimensional random spanning trees

A spanning tree of a finite connected graph G is a connected subgraph of G that touches every vertex and contains no cycles. In this talk we will consider uniformly drawn spanning trees of high-dimensional graphs, and show that, under appropriate rescaling, they converge in distribution as metric-measure spaces to Aldous’ Brownian CRT. This extends an earlier result of Peres and Revelle (2004) who previously showed a form of finite-dimensional convergence. If time permits, we may also discuss scaling limits of random spanning trees with non-uniform laws. Based on joint works with Asaf Nachmias and Matan Shalev.

Monday 23rd of October: Martin Vogel (Strasbourg)

Emergence of Gaussian fields in noisy quantum chaotic dynamics

The theory of quantum chaos aims to describe quantum mechanical states in an environment where the classical dynamics is chaotic. The guiding example is the Laplace-Beltrami operator on a compact hyperbolic smooth manifold and it is conjectured by Rudnick and Sarnack that the underlying chaotic classical dynamics on such manifolds results in delocalization properties of the eigenfunctions of the Laplace-Beltrami operator. In this talk, we shall consider a toy model for this: we will show how Lagrangian states propagated by the semi-group induced by a suitable random Schrödinger operator converge locally to a stationary monochromatic isotropic Gaussian field. 

This is joint work with M. Ingremeau.

Monday 16th of October : Ulrik Hansen (Fribourg)

  On The Number of Percolation Phase Transitions In The Ising Model

The Ising model is among the richest objects of study in statistical mechanics. One reason for this is its zoo of graphical representations, from the high temperature and random current expansions to its FK representation. Each of these models sees correlations in the Ising model through their connectivity properties and so, a very natural question suggests itself: Namely, whether their connectivity properties change jointly or not - for instance, whether the three models have an onset of percolation at the same temperature.

 In '18, Garet, Marchand and Marcovici showed that the high temperature expansion on Z^2 has a percolation phase transition at the Ising critical temperature, and by a result of Lupu and Werner, the same result follows for the random current. With the same techniques, however, one may prove that the high temperature expansion never percolates on the hexagonal lattice. Thus, the answer to the question outlined above is not as clear-cut as one might hope.

 In this talk, we will turn our attention to the higher dimensional case of Z^d for d at least 3. Here, we will use a coupling between the high temperature expansion and the random-cluster model due to Grimmett and Janson, which presents the former as a uniform even subgraph of the latter. This coupling then allows us to a) utilise a famous argument due to Kozma and Sidoravicius to show that the high temperature expansion exhibits long loops on the torus throughout the supercritical regime and b) show a mixing property of the uniform even graph, which allows us to compare the model on the torus to the model on Z^d.

Based on joint work with Boris Kjær and Frederik Ravn Klausen.

Monday 9th of October : Vikram Giri (ETH)

  Turbulence and Nash iteration

 In the phenomenological theory of turbulence, ``statistical ensembles'' of fluid flows that obey certain symmetries are assumed to exist from which one derives various properties of the flow. In the absence of a mathematical rigorous foundation to this theory, one can ask the basic question of whether the incompressible fluid equations allow for solutions that exhibit anomalous dissipation and intermittency, two of the basic and well-established phenomena in 3 dimensional fully-developed turbulence. In the context of the incompressible Euler equations, we will use a Nash iteration, which had its origins in the problem of isometrically embedding Riemannian manifolds, to show the existence of such ``turbulent'' solutions. This is joint work with Hyunju Kwon and Matthew Novack. I will try to explain the background and concepts involved and the talk should be accessible to all. 

Monday 2nd of October : Florian Schweiger (Unige) 

 The maximum of log-correlated Gaussian fields in random environment 

In recent years there has been a lot of progress in studying the extrema of logarithmically correlated random fields. In the talk I will review some of the results in the area, and then discuss an extension to log-correlated Gaussian fields in an environment that is itself random. One key example is the two-dimensional Gaussian free field on a supercritical bond percolation cluster. In order to study such models, one needs to combine tools from quantitative stochastic homogenization and classical probabilistic estimates for branching structures.
Based on joint work with Ofer Zeitouni. 

Monday, 19th of June: Nicolas Curien (Orsay)

 Ideal Poisson-Voronoi tiling 

We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces. In contrast to the Euclidean setting, a limiting non-trivial ideal tessellation appears as the intensity tends to 0. The tessellation obtained is a natural Möbius-invariant decomposition of the hyperbolic space into countably many infinite convex polytopes, each with a unique end.  We study its basic properties, in particular the geometric features of its cells.
Based on joint works with Matteo d'Achille, Nathanael Enriquez, Russell Lyons and Meltem Unel.

Monday, 12th of June: Nathanael Berestycki (Vienna)

 Near-critical dimers and massive SLE

A programme initiated by Makarov and Smirnov is to describe near-critical scaling limits of planar statistical mechanics models in terms of massive SLE and/or Gaussian free field. We consider here the dimer model on the square or hexagonal lattice with doubly periodic weights, which is known to have non Gaussian limits in the whole plane. In joint work with Levi Haunschmid (TU Vienna) we obtain the following results: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov; (b) we show that the convergence of the height function in arbitrary bounded domains subject to Temperleyan boundary conditions, and that the scaling limit is universal; and (c) we prove conformal covariance of the scaling limit. Our techniques rely on Temperley's bijection and the "imaginary geometry" approach developed in earlier work with Benoit Laslier and Gourab Ray, as well as a new exact discrete Girsanov identity on the triangular lattice. Time-permitting we will discuss conjectures relating this model to the sine-Gordon model. 

Tuesday, 30th of May: Eveliina Peltola (Aalto & Bonn)

On large deviations of SLEs, real rational functions, and zeta-regularized determinants of Laplacians

When studying large deviations (LDP) of Schramm-Loewner evolution (SLE) curves, a ''Loewner energy", and "Loewner potential'', that describe the rate function for the LDP, were recently introduced. While these objects were originally derived from SLE theory, they turned out to have several intrinsic, and perhaps surprising, connections to various fields. I will discuss some of these connections and interpretations towards Brownian loops, semiclassical limits of certain correlation functions in conformal field theory, and rational functions with real critical points (Shapiro-Shapiro conjecture in real enumerative geometry).

Based on joint work with Yilin Wang (IHES).

Monday, 22th of May: Amanda Turner (Leeds)

A statistical mechanics approach to planar aggregation

Planar random growth processes occur widely in the physical world. Examples include diffusion-limited aggregation (DLA) for mineral deposition and the Eden model for biological cell growth. One approach to mathematically modelling such processes is to represent the randomly growing clusters as compositions of conformal mappings. The Aggregate Loewner Evolution (ALE) model, formulated in this way,  provides a means of interpolating between the Eden model and DLA through varying a single parameter. An intriguing property is a conjectured phase transition between models that converge to growing disks, and 'turbulent' non-disk like models, but as yet there is no satisfactory explanation for this phenomenon. In this talk I will show how ALE can be formulated as a statistical mechanics model which provides a possible framework in which to explore the existence of phase transitions.

Monday, 15th of May: Ajay Chandra (Imperial College) & Ilya Chevyrev (Edinburgh)

Loop expansions for lattice gauge theories

In this two-part talk, we will present a loop expansion for lattice gauge theories and show how it applies to show ultraviolet stability in the Abelian Higgs model. In the first part, we will describe the loop expansion and related works of Brydges-Frohlich-Seiler. In the second part, we will show how the expansion can be applied to obtain a quantitative diamagnetic inequality. Combined with suitable lattice gauge fixing, the diamagnetic inequality allows us to show moment bounds on the gauge field marginal, uniform in the lattice spacing, when measured in Holder-Besov-type spaces. 

Monday, 8th of May: Alain Joye (Grenoble)

Mathematical (De-)Localisation for the Chalker-Coddington Model

The Chalker-Coddington model is a simplified, discrete version of the quantum dynamics of an electron in the plane submitted to a random potential and strong magnetic field. After a description of its construction and main properties, we shall review some mathematical results regarding the localisation and transport properties of the Chalker-Coddington model in various setups.

Tuesday, 2nd of May: Scott Armstrong (NYU)

Quantitative homogenization in high contrast

Consider the random conductance model on the Zd lattice where the conductivity function is iid and bounded between two positive constants. There has been a lot of work in recent years in developing very fine quantitative estimates for the behavior of harmonic functions (or equivalently, random walks) on large scales. These estimates are sharp in the limit of asymptotic scale separation. They however depend very badly on the "ellipticity contrast," that is, the ratio of largest to smallest possible value of the conductivities. It is an open problem to develop non-ridiculous estimates for the length scale at which homogenization begins to be seen, as a function of the ellipticity contrast. I will present a first result in this direction, and compare it to some estimates in percolation theory. (Joint work with Tuomo Kuusi.)

Tuesday, 2nd of May: Sylvia Serfaty (NYU)

Recent developments on Coulomb gases

  We will present a review on results on the Coulomb gas in general dimension: local laws describing the system down to micro scale, LDP for empirical field, CLT for fluctuations and hyper uniformity in dimension 2.

Monday, 24th of March: Steffen Polzer (Unige)

Renewal approach for the energy-momentum relation of the Polaron

The Fröhlich polaron is a model for the interaction of an electron with a polar crystal. We study the energy-momentum relation E(P) which is the bottom of the spectrum of the fixed total momentum Hamiltonian H(P). An application of the Feynman-Kac formula leads to Brownian motion perturbed by a pair potential. The point process representation introduced by Mukherjee and Varadhan represents this path measure as a mixture of Gaussian measures, the respective mixing measure can be interpreted in terms of a perturbed birth and death process. We apply the renewal structure of this point process representation in order to obtain a representation of a diagonal element of the resolvent of H(P). This then yields several properties of the energy-momentum relation, such as monotonicity in |P| and that the correction to the quasi-particle energy is negative.

Monday, 17th of April: Franco Severo (ETHZ)

On the size of level-set components for strongly correlated Gaussian fields

We study the level-sets of smooth Gaussian fields on R^d with slow decay of correlations (i.e. algebraic decay with exponent smaller than 1). As the level varies, this defines a percolation model, for which we compute the exact exponential rate of decay in probability for the size of subcritical connected components. This rate turns out to be proportional to the inverse correlation times the square of the distance to the critical level. This differs drastically from fields with fast decay of correlations, for which the cluster size probability always decays exponentially, and the precise rate constant is not well understood. Our result is an evidence in support of physicists' predictions for the characteristic length exponent of fields with slow algebraic decay of correlations, and also opens to way to the study of other large deviations questions for smooth Gaussian fields. In this talk, I aim at explaining how the existence of strong correlations leads to a (perhaps surprisingly) better understanding of these large deviation questions. This is based on a joint work with Stephen Muirhead.

Monday, 3rd of April: Martin Hairer (EPFL)

Renormalisation & Symmetries

Monday, 27th of March: Tyler Helmuth (Durham)

The Arboreal Gas

In Bernoulli bond percolation each edge of a graph is declared open with probability p, and closed otherwise. Typically one asks questions about the geometry of the random subgraph of open edges. The arboreal gas is the probability measure obtained by conditioning on the event that the percolation subgraph is a forest, i.e., contains no cycles. Physically, this is a model for studying the gelation of branched polymers. Mathematically it is the q->0 limit of the random cluster model. What are the percolative properties of these random forests? Do they contain giant trees? I will discuss what is known, what is conjectured, and how a connection with spin systems allows for analysis and intuition.

Monday, 20th of March: Nikolay Barashkov (Helsinki)

The $\phi^4_3$ model and towards Segal's axioms

The $\phi^4_3$ model is a 3-dimensional non-Gaussian Euclidean QFT. Showing existence of such a measure was one of the highlights of the constructive QFT programme in the '70s. In this talk I will describe joint work with Trishen Gunaratnam in analysing how different $\phi^4_3$ models glue together on cylinders.

Monday, 13th of March: Pierre Germain (Imperial)

Weak turbulence and the wave kinetic equation

The wave kinetic equation is expected to provide a description of weak turbulence, which is the chaotic dynamics appearing in weakly nonlinear systems. This (deterministic) kinetic equation should describe energy transfer between scales, and provides an entrypoint into the (random) world of turbulence. I will present these ideas and recent progress in this area.

Monday, 6th of March: Paul Dario (CNRS, UPEC)
Localization and delocalization for a class of degenerate convex grad phi interface model

In this talk, we will consider a classical model of random interfaces known as the grad phi (or Ginzburg-Landau) model. The model first received rigorous consideration in the work of Brascamp-Lieb-Lebowitz in 1975. Since then, it has been extensively studied by the mathematical community and various aspects of the model have been investigated regarding for instance the localization and delocalization of the interface, the hydrodynamical limit, the scaling limit, large deviations etc.  Most of these results were originally established under the assumption that the potential encoding the definition of the model is uniformly convex, and it has been an active line of research to extend these results beyond the assumption of uniform convexity. In this talk, we will introduce the model, some of its main properties, and discuss a result of localization and delocalization for a class of convex (but not uniformly convex) potentials.

Monday, 27th of February: Sungchul Park (KIAS)

Analysis of the planar Ising model under massive scaling limit

We give an overview of recent convergence results for the Ising model in two dimensions under a massive scaling limit, including convergence of spin and energy correlations and martingale observables for its interfaces. In particular, we highlight the analytical ideas used to deal with different boundary conditions and directions of perturbation, in the presence of possibly rough boundary segments. Based on joint works with Chelkak, Wan, and others.

Monday, 06th of February: Ariel Perez Mellor (UNIGE)

Using Graph Theory to Unravel Born Oppenheimer Molecular Dynamics and Replica-Exchange Monte Carlo Simulation 

In this seminar, I intend to introduce to you how graph theory analysis can be applied in the field of theoretical chemistry. I will discuss the treatment of a set Born-Oppenheimer molecular dynamics and a replica-exchange Monte Carlo trajectories. The first part of the talk will be dedicated to laying the foundations of the methodology by defining the necessary mathematical objects [1]. It includes the definition of colored graphs and their representation through the adjacency matrix together with the introduction of some properties that they must fulfil. At this point, I will discuss the isomorphism problem that arises when two identical atoms are swapped and how it can be solved. The second part will be devoted to the applications of the methodology. I will bring your attention to understanding the complex gas phase dissociation dynamics of three systems: the protonated cyclo Gly-Gly and the naphthalene and azulene cations. Finally, I will explain how the methodology can be extended to the analysis of a set of replica-exchange Monte-Carlo trajectories. 

Tuesday, 20th of December: Benoit Collins (Kyoto University)

New results around the norm of random matrices and operator-valued non-backtracking theory 

Non-backtracking operators have long ago proved to be very useful in (random) graph theory, e.g., in the study of (almost) Ramanujan graphs. A couple of years ago, we noticed that this theory extends in various directions: (1) uniformly equal coefficients of the operator can be replaced by matrix-valued coefficients to handle much more general adjacency matrices (thanks to a linearization trick), (2) the very generators of the non-backtracking operators, that were initially permutations, can be replaced by arbitrary unitary operators. We will report on recent progress along these lines, with new applications to random matrix theory and operator algebra. Time allowing I will also elaborate on the theory of “linearization tricks”, including new results for unitary operators. This work is based on past and ongoing work with Charles Bordenave.

Monday, 12th of December: Piet Lammers (IHES)

Planarity, percolation, and height functions

Fröhlich and Spencer proved the Berezinskii-Kosterlitz-Thouless transition in 1981, through a relation with delocalisation of height functions. My talk focuses on the phase transition for height functions. We mix ideas coming from height functions and planar percolation models in order to prove a coarse-graining inequality inspired by the renormalisation group picture. This allows us to make precise statements about the phase transition (e.g. sharpness) even without knowing exactly where this transition point lies. This talk is based on the recent preprint arXiv:2211.14365. 

Monday, 5th of December: Sébastien Martineau (UPMC)

Percolation on homogeneous graphs of polynomial growth 

Bernoulli percolation consists in erasing independently each edge of a graph G with some probability 1-p and studying the connected components (called clusters) of this random graph. Of interest is the parameter pc(G) above which infinite clusters exist. In this talk, we focus on homogeneous (= transitive) graphs for which the cardinality of balls is upper-bounded by a polynomial function of the radius. For such graphs, we get a good understanding of the supercritical regime p>pc (supercritical sharpness). From this, we deduce that Schramm's locality conjecture holds for such graphs: if you give me a ball of radius 10^10 of such a graph G, it is in principle possible for me to tell you "either pc(G)=1 or pc(G) is very close to [some specific value depending on the ball]". This is joint work with Daniel Contreras and Vincent Tassion.

Monday, 28th of November: Giuseppe Cannizzaro (Warwick)

Diffusion in the curl of the two-dimensional Gaussian Free Field 

I will discuss the large time behaviour of a Brownian diffusion in two dimensions, whose drift is divergence-free and ergodic, and given by the curl of the two-dimensional Gaussian Free Field. Together with L. Haundschmid and F. Toninelli, we prove the conjecture by B. Tóth and B. Valkó that the mean square displacement is of order $t \sqrt{\log t}$. The same type of superdiffusive behaviour has been predicted to occur for a wide variety of (self)-interacting diffusions in dimension d = 2, including the diffusion of a tracer particle in a fluid, self-repelling polymers and random walks, Brownian particles in divergence-free random environments, and, more recently, the 2-dimensional critical Anisotropic KPZ equation. To the best of our knowledge, ours is the first instance in which $\sqrt{\log t}$-superdiffusion is rigorously established in this universality class. 

Monday, 21st of November: Charles Bordenave (CNRS - Institut mathématique de Marseille) 

Mobility Edge of Lévy Matrices 

This is a joint work with Amol Aggarwal and Patrick Lopatto. Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an α-stable law. For α<1, predictions from the physics literature suggest that high-dimensional Lévy matrices should display the following phase transition at a point Emob. Eigenvectors corresponding to eigenvalues in (−Emob,Emob) should be delocalized, while eigenvectors corresponding to eigenvalues outside of this interval should be localized. Further, Emob is given by the (presumably unique) positive solution to λ(E,α)=1, where λ is an explicit function of E and α.

We prove the following results about high-dimensional Lévy matrices.

(1) If λ(E,α)>1 then eigenvectors with eigenvalues near E are delocalized.

(2) If E is in the connected components of the set {x:λ(x,α)<1} containing ±∞, then eigenvectors with eigenvalues near E are localized.

(3) For α sufficiently near 0 or 1, there is a unique positive solution E=Emob to λ(E,α)=1, demonstrating the existence of a (unique) phase transition.

(a) If α is close to 0, then Emob scales approximately as |logα|^(−2/α).

(b) If α is close to 1, then Emob scales as (1−α)^(−1).

Our proofs proceed through an analysis of the local weak limit of a Lévy matrix, given by a certain infinite-dimensional, heavy-tailed operator on the Poisson weighted infinite tree. 

Monday, 14th of November: Dmitri Krachun (UNIGE)

Blume Capel model on Z^d

The Blume-Capel model can be seen as a natural generalisation of the Ising model, where spins are allowed to take value in $\{-1, 0, 1\}$. In this talk I will introduce the model and discuss its conjectural phase diagram as well as some classical and new connections to the Ising model. While presenting the main ideas of the proofs concerning the behaviour of the model on $\mathbb{Z}^d$, I will show how many beautiful probabilistic techniques developed over the last decades to study Ising and percolation models allow to rigorously study various regimes of the Blume-Capel model and its phase transition. Based on joint work with Trishen Gunaratnam and Christoforos Panagiotis 

Monday, 7th of November: Juhan Aru (EPFL)

A Green's function for CLE_4 and twist fields of the 2d GFF 

We will discuss how exploring and exploiting connections between CLE_4, GFF and loop soups can help rediscover old formulas appearing in  c = 1 conformal field theories related to the critical Ashkin-Teller model(s). This is joint work with F. Gabriel and T. Lupu. 

Monday, 17th of October 2022: Laurin Köhler-Schindler (ETHZ)

Scaling limits and arm exponents for the planar fuzzy Potts model

The fuzzy Potts model is obtained by independently coloring the clusters of a Fortuin-Kasteleyn (FK) percolation. We study the model on the square lattice when the FK percolation is critical. Under the assumption that this critical FK percolation converges to a conformally invariant scaling limit (which is known to hold for the FK-Ising model), we show that the obtained coloring converges to variants of Conformal Loop Ensembles constructed, described and studied by Miller, Sheffield and Werner. Using discrete considerations, we also show that the arm exponents for this coloring in the discrete model are identical to the ones of the continuum model. This allows us to determine the arm exponents for the planar fuzzy Potts model. Joint work with Matthis Lehmkuehler. 

Monday, 10th of October 2022: Barbara Dembin (ETHZ)

Almost sharp sharpness for Boolean percolation

We consider a Poisson point process on $\mathbb R ^d$ with intensity $\lambda$ for $d\ge2$. On each point, we independently center a ball whose radius is distributed according to some power-law distribution $\mu$. When the distribution $\mu$ has a finite $d$-moment, there exists a non-trivial phase transition in $\lambda$ associated to the existence of an infinite connected component of balls. We aim here to prove subcritical sharpness that is that the subcritical regime behaves well in some sense. For distribution $\mu$ with a finite $5d−3$-moment, Duminil-Copin--Raoufi--Tassion proved subcritical sharpness using randomized algorithm. We prove here using different methods that the subcritical regime is sharp for all but a countable number of power-law distributions.

Joint work with Vincent Tassion.  

Monday, 3rd of October 2022: Alexis Prévost (UNIGE)

Critical exponents for a percolation model on transient graphs

I will present some conjectures about critical exponents for percolation models with long-range correlations, and explain how these conjectures are solved in the specific case of level sets percolation for the Gaussian free field on the cable system. An essential role will be played by a certain capacity functional of the level sets, which appear naturally in a differential formula associated with this model. In particular, one can explicitly compute the law of the capacity of bounded clusters, and deduce asymptotics for various quantities in the critical or near-critical regime, such as the percolation probability or two points function. The talk is based on joint work with Alexander Drewitz and Pierre-François Rodriguez.  

Monday, 26th of September 2022: Benoit Dagallier (Cambridge)

Log-Sobolev inequality for the continuum phi^4_2 and phi^4_3 models

In this talk, I will report on a joint work with Roland Bauerschmidt in which we analyse the Langevin dynamics associated with the continuum phi4 model. The continuum phi4 model is one of the simplest models of field theory, introduced at least 50 years ago in the physics community. It can be thought of as a continuous analogue of the Ising model. In particular, it exhibits a phase transition, separating a weakly correlated and a strongly correlated regime. The presence of a phase transition should imply a dramatic difference in how much time it takes for the dynamics to approach its steady state, from fast convergence above the critical point, to slow convergence diverging with the system size below it. The analysis of the model is made particularly subtle due to the fact that the continuum limit is ill-defined, in the sense that a certain renormalisation procedure is needed to make sense of it. We characterise the relaxation to the steady state by proving a logarithmic Sobolev inequality (LSI) with constant bounded under optimal assumptions. The proof makes use of a very general LSI criterion developed in 2019 by Roland Bauerschmidt and Thierry Bodineau. 

In the talk, I will introduce the phi4 model and LSI inequalities, then try to explain the main ideas as non-technically as possible. 

Monday, 19th of September 2022: Aymeric Perriard (UNIGE)

Observation of the abelian sandpile model from numerical simulations

We will first present the Abelian sandpile model.  We will then look numerically at the behaviour of the one-dimensional model, and complexify it little by little to reach the two-dimensional rectangular lattice. For each graph, we observed the numerical distribution of avalanches and tried to understand why and how the distributions converge to a power law. Finally, we will look at the behaviour of the model and in particular the avalanche geometry for a particular graph "halfway" between the one and two dimensional graph. 

25/05/22. Yannick Couzinie

16/05/22. Lucas D'Alimonte and Romain Panis

02/05/22. John Haslegrave

25/04/22. Arnaud Le Ny

11/04/22. Pierre-François Rodriguez

04/04/22. Gady Kozma

28/03/22. Guillaume Baverez

21/03/22. Rémy Mahfouf

14/03/22. Nikolay Barashkov and Michael Hofstetter

07/03/22. Larissa Richards

26/01/22. Yonatan Gutman

13/12/21. Marcin Lis

29/11/21. Jian Ding and Jian Song

22/11/21. Christophe Garban

15/11/21. Maxime Savoy

08/11/21. Nikos Zygouras

01/11/21. Ewain Gwynne

25/10/21. Vittoria Silvestre

18/10/21. Daniel Sanchez

22/11/2021. Christophe Garban (ENS Lyon)

Continuous symmetry breaking along the Nishimori line

15/06/2020. Speaker: Yacine Aoun

Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models 

25/05/2020. Speaker: Paul Melotti

The eight-vertex model via dimers

18/05/2020. Speaker: Antti Knowles

Field theory as a limit of interacting quantum Bose gases

11/05/2020. Speaker: Simone Warzel

Mean-Field Quantum Spin Glasses

04/05/2020. Speaker: Franco Severo

On the diameter of Gaussian free field excursion clusters away from criticality

27/04/2020. Speaker: Christophe Garban

Kosterlitz-Thouless transition and statistical reconstruction of the Gaussian free field

20/04/2020. Speaker: Thomas Leblanc

Two "physical" characterizations of the Sine-beta process

30/03/2020. Speaker: Hugo Duminil-Copin

Gaussianity of the 4D Ising model

09/03/2020. Speaker: Charles Bordenave

Strong asymptotic freeness for representations of independent Haar unitary matrices 

02/03/2020. Speaker: Raphaël Bucatez

Outliers for zeros of random polynomials and Coulomb gases

17/02/2020. Speaker: Marianna Russkikh

Dimers and embeddings

16/12/2019. Speaker: Lucas Benigni

Fermionic eigenvector moment flow 

02/12/2019. Speaker: Christopher J. Bishop

Weil-Petersson curves and finite total curvature.

02/12/2019. Speaker: Vieri Mastropietro

Renormalization Group approach to universality in non-integrable systems

25/11/2019. Speaker: Izabella Stuhl

The hard-core model in discrete 2D: ground states, dominance, Gibbs measures

18/11/2019. Speaker: Mikhail Khristoforov

Discrete multi-point and vector-valued observables in percolation.

12/11/2019. Speaker: Tyler Helmuth

Random spanning forests and hyperbolic symmetry

11/11/2019. Speaker: Nicolai Reshetikhin

Limit shapes in statistical mechanics

04/11/2019. Speaker: Christian Webb

How much can the eigenvalues of a random Hermitian matrix fluctuate?

28/10/2019. Speaker: Alessandro Olgiati

Stability of the Laughlin phase in presence of interactions

21/10/2019. Speaker: Daniel Lenz

Spectral theory of one-dimensional quasicrystals

14/10/2019. Speaker: Phan Thành Nam

Nonlinear Gibbs measures as the limit of equilibrium quantum Bose gases

07/10/2019. Speaker: Jonathan Hermon

Anchored expansion in supercritical percolation on nonamenable graphs

30/09/2019. Speaker: Vittoria Silvestri

Fluctuations and mixing of Internal DLA on cylinders

23/09/2019. Speaker: Dominik Schröder

Edge Universality for non-Hermitian Random Matrices

16/09/2019. Speaker: Antti Knowles

Expander graphs and the spectral gap of random regular graphs

27/05/2019. Speaker: Roland Bauerschmidt

Log-Sobolev inequalities for some strongly correlated spin systems

21/05/2019. Speaker: Tom Hutchcroft

Percolation critical exponents inequalities via randomised algorithms

13/05/2019. Speaker: Lukas Schoug

Dimensions of the two-valued sets of the 2D GFF

06/05/2019. Speaker: Eero Saksman

Decompositions of log-correlated fields with applications

29/04/2019. Speaker: Karen Habermann

A semicircle law and decorrelation for iterated Kolmogorov loops

15/04/2019. Speaker: Roman Boykiy

Dimensions of LQG-type random maps

08/04/2019. Speaker: Janne Junnila

Imaginary multiplicative chaos and the XOR-Ising model

01/04/2019. Speaker: Jean-Pierre Eckmann

Hamiltonian breathers with dissipation

25/03/2019. Speaker: Noam Berger

Moment estimates for regenerations in RWRE in the absence of a zero-one law

18/03/2019. Speaker: Ellen Powell

Welding critical LQG surfaces

11/03/2019. Speaker: Pierre Collet

Time scales in some large population birth and death processes, quasistationary distribution and resilience

04/03/2019. Speaker: Franck Gabriel

Neural Tangent Kernel: Convergence and Generalization in Neural Networks (joint work with Arthur Jacot and Clément Hongler)

25/02/2019. Speaker: Eveliina Peltola

Crossing probabilities of multiple Ising interfaces

17/12/2018. Speaker: Giovanni Antinucci

A Hierarchical Supersymmetric Model for Weakly Disordered 3d Semimetals 

10/12/2018. Speaker: Alain Joye

Representations of canonical commutation relations describing infinite coherent states

26/11/2018. Speaker: Mikhail Basok

Tau-functions a la Dubedat and cylindrical events in the double-dimer model

19/11/2018. Speaker: David Belius

The TAP-Plefka variational principle for mean field spin glasses

12/11/2018. Speaker: Damien Gayet

Percolation without FKG 

05/11/2018. Speaker: Benoit Laslier

Logarithmic variance for uniform homomorphisms on Z^2 

29/10/2018 and 30/10/2018.

SPECIAL EVENT: 4 x 45min lectures by Yilin Wang

Monday 29.10, 15:15-16:00 and 16:45-17:00, ACACIAS, SM17

Tuesday 30.10, 15:00-15:45 and 16:15-17:00, ACACIAS, SwissMap Meeting Room, 3rd floor

The Loewner energy at the crossroad of random geometry, geometric function theory, and Teichmueller theory

22/10/2018. Speaker: Jiri Cerny

The maximal particle of branching random walk in random environment

15/10/2018. Speaker: Raphael Ducatez

Anderson model and random products of matrices

08/10/2018. Speaker: Thomas Budzinski

Supercritical causal maps: geodesics and simple random walk

01/10/2018. Speaker: Hugo Vanneuville

Level set percolation for Gaussian fields

24/09/2018. Speaker: Alexander Glazman

Random Lipschitz functions and 6-vertex model via spin representations

19/02/2018. Speaker: Misha Khristoforov

Title: An order/disorder perturbation of percolation model. A highroad to Cardy's formula.

26/02/2018. Speaker: Gaultier Lambert

Title: Stein's method for normal approximation of linear statistics of beta-ensembles

Slides

05/03/2018. Speaker: Lorenz Hilfiker

Title: Solutions to Thermodynamic Bethe Ansatz equations and Y-systems

12/03/2018. Speaker: Sasha Sodin

Title: Non-Hermitian random Schroedinger operators

26/03/2018. Speaker: Alessandro Giuliani

Title: Plate-nematic phase in a 3D hard-core particle system

09/04/2018. Speaker: Thierry Bodineau

Title: Perturbative regimes for deterministic dynamics of a diluted gas of hard spheres

16/04/2018. Speaker: Yilin Wang

Title: The Loewner energy of a simply connected domain on the Riemann sphere

23/04/2018. Speaker: Pierre Youssef

Title: On the norm of Gaussian random matrices

07/05/2018. Speaker: Nathanael Berestycki

Title: Dimer model on surfaces

14/05/2018. Speaker: Konstantin Izyurov

Title: Scaling limits of critical Ising correlations: convergence, fusion rules, applications to SLE

28/05/2018. Speaker: Alex Karrila

Title: Boundary visits of loop-erased random walks

04/06/2018. Speaker: Marcin Lis

Title: The double random current nesting field

Slides 

25/09/2017. Speaker: Alexander Glazman

Title: Phase transition in the loop O(n) model

02/10/2017. Speaker: Sung Chul Park

Title: Ising Model: Local Spin Correlations and Conformal Invariance

09/10/2017. Speaker: Yvan Velenik

Title: Ornstein-Zernike theory of Ising and Potts models: a review of some applications

16/10/2017. Speaker: Joonas Turunen

Title: Critical Ising model on infinite random triangulation of the half plane

06/11/2017. Speaker: Alexey Bufetov

Title: Stochastic vertex models and symmetric functions

Slides

13/11/2017. Speaker: Christophe Pittet

Title: Convergence rates in von Neumann ergodic theorems for free groups

20/11/2017. Speaker: Hao Wu

Title: Hypergeometric SLE and Convergence of Critical Planar Ising Interfaces

Slides

27/11/2017. Speaker: Ananth Sridhar

Title: Limit Shapes in the Stochastic Six Vertex Model

04/12/2017. Speaker: Johannes Alt

Title: Local inhomogeneous circular law

Slides

11/12/2017. Speaker: Sanjay Ramassamy

Title: Miquel dynamics on circle patterns

Slides

18/12/2017. Speaker: Daniel Ueltschi

Title: Random interchange model on the complete graph and the Poisson-Dirichlet distribution 

26/06/2017. Speaker: Vaughan Jones

Title: On scale invariance states of quantum spin chains

12/06/2017. Speaker: Nicolas Rougerie

Title: Fractional quantum Hall effect and generalized Coulomb gases

29/05/2017. Speaker: Noemi Kurt

Title: Mathematical population genetics and the seed bank coalescent

22/05/2017. Speaker: Andrea Agazzi

Title: Large Deviations Theory for Chemical Reaction Networks

15/05/2017. Speaker: Victor Kleptsyn

Title: Furstenberg theorem with a parameter and Anderson localization in dimension one

08/05/2017. Speaker: Kalle Kytölä

Title: Conformal field theory on lattice: from discrete complex analysis to Virasoro algebra

24/04/2017. Speaker: Fredrik Viklund

Title: Loop-erased walks and natural parametrization

10/04/2017. Speaker: Kevin Schnelli

Title: Addition of random matrices

06/04/2017. Speaker: Marianna Russkikh

Title: Playing dominos in different domains

03/04/2017. Speaker: Francis Comets

Title: Cover time for the random walk and Brownian motion on the two-dimensional torus and random interlacement

27/03/2017. Speaker: Margherita Disertori

Title: Some results on history dependent stochastic processes

13/03/2017. Speaker: Giambattista Giacomin

Title: Disorder and depinning transitions: the lattice free field case

06/03/2017. Speaker: Vincent Vargas

Title: An Introduction to Liouville Conformal Field Theory

27/02/2017. Speaker: Ellen Powell

Title: Critical branching diffusions in bounded domains

23/02/2017. Speaker: Yuri Kifer

Title: Some Extensions Of The Erdos-Renyi Law Of Large Numbers

20/02/2017. Speaker: Vadim Gorin

Title: Universal local limits for lozenge tilings and noncolliding random walks 

19/12/2016. Speaker: Felix Gunther

Title: Discrete complex analysis and discrete Riemann surfaces

12/12/2016. Speaker: Igor Krasovsky

Title: Splitting of a gap in the bulk of the spectrum of random matrices

05/12/2016. Speaker: Juhan Aru (ETHZ)

Title: Bounded-type local sets for the 2D Gaussian free field

28/11/2016. Speaker: Adrien Kassel

Title: A geometrical take on isomorphism theorems for random walks

21/11/2016. Speaker: Ismael Bailleul

Title: Singular PDEs

14/11/2016. Speaker: Matteo Marcozzi

Title: Non-Gaussian Wick polynomials and cumulants in kinetic theory

07/11/2016. Speaker: Antti Knowles

Title: Local laws as a gateway to the eigenvalue and eigenvector statistics of random matrices

31/10/2016. Speaker: Jakob Bjornberg

Title: Probabilistic methods for quantum spin systems

24/10/2016. Speaker: Vincent Beffara

Title: Percolation of random nodal lines

17/10/2016. Speaker: Wei Qian. (ETHZ)

Title: Decomposition of Brownian loop-soup clusters

10/10/2016. Speaker: Fabio Toninelli

Title: A class of (2+1)-dimensional growth process with explicit stationary measure

03/10/2016. Speaker: Jean-Christophe Mourrat

Title: Heat kernel upper bounds for interacting particle systems

26/09/2016. Speaker: Titus Lupu

Title: What the cable graph techniques can tell about the continuum Gaussian Free Field in dimension 2

19/09/2016. Speaker: Eveliina Peltola

Title: On correlation functions, scaling limits, and Schramm-Loewner evolutions 

Lundi 18 avril 2016: Sébastien Martineau (Weizmann Institute)

Lundi 11 avril 2016: Antal Jarai

Lundi 21 mars 2016: Gourab Ray (University of Cambridge) Universality for fluctuation in the dimer model.

Lundi 14 mars 2016: Tobias Müller (Utrecht University) The critical probability for confetti percolation equals 1/2 

Lundi 07 mars 2016: Alessandra Caraceni (Paris Sud) A stroll around Random Infinite Quadrangulations of the Plane 

Lundi 29 Février 2016: Camille Male (Paris 5) A free probability theory for permutation invariant random graphs and matrices 

Lundi 07 décembre: conférence in CIB

Lundi 30 novembre 2015: Nicolas Orantin (EPFL) Solving loop models on random lattices.

Lundi 23 novembre 2015: Benjamin Schlein (university of Zurich) Hartree-Fock dynamics for weakly interacting fermions

Lundi 16 novembre 2015: journée Lyon-Genève-Grenoble 

Lundi 09 novembre 2015: Nikolaos Zygouras (Warwick) Scaling limits of disordered systems: disorder relevance and universality.

Lundi 02 novembre 2015: Piotr Milos (Warsaw) Delocalization of two-dimensional random surfaces with hard-core constraints 

Lundi 26 octobre 2015: Noé Cuneo (Unige) Non-equilibrium steady states for chains of rotors

Lundi 19 octobre 2015: Daniel Ahlberg (IMPA) Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome?

Lundi 12 octobre 2015: Vadim Kaloshin (University of Maryland) Stochastic Arnold diffusion of deterministic systems

Lundi 05 octobre 2015: conférence CIB

Lundi 28 septembre 2015: Dmitry Chelkak and David Cimasoni (Unige) On the combinatorics of the 2D Ising model

Lundi 21 septembre (talk in english) 2015: Viviane Baladi (ENS) Mélange exponentiel des flots billards de Sinai 

Mardi 15 septembre 2015: Dmitry Ioffe (technion) Effective model of facets formation and ordered walks under area tilts

Vendredi 11 septembre 2015: Michael Aizenman (Princeton) Ising model from the Random Current prospective

Lundi 24 aout 2015: Alexander Fribergh (university of Montreal) The ant in “a" labyrinth

06/07/2015. Speaker: Augusto Teixeira

Title: Percolation and local isoperimetric inequalities

15/04/2015. Speaker: Gabor Pete

Title: Noise sensitivity questions in percolation-like processes

16/03/2015. Speaker: Neal Madras

Title: Random Pattern-Avoiding Permutations

02/03/2015. Speaker: Bruno Benedetti

Title: Discrete Morse theory and the number of triangulated manifolds

23/02/2015. Speaker: Mikhail Shkolnikov

Title: Tropical curves from sandpiles 

15/12/2014. Speaker: Pierre-Louis Giscard

Title: Compactness and large deviations

08/12/2014. Speaker: Nicolas Rougerie

Classical Coulomb gases: mean-field approximation and beyond

24/11/2014. Speaker: Fabio Toninelli

Title: Entropic repulsion, metastability and large deviations for SOS interfaces

17/11/2014. Speaker: Antti Knowles

Title: Anisotropic local laws for random matrices

12/11/2014. Speaker: Patrik Ferrari

Title: Free energy fluctuations for directed polymers in 1+1 dimension

03/11/2014. Speaker: Alessandro Giuliani

Title: Height fluctuations in interacting dimers

27/10/2014. Speaker: Benoit Laslier

Title: Dynamique stochastique d'interface discrète et modèles de dimères

20/10/2014. Speaker:  Esa Järvenpää 

Title: Dimensions of random covering sets in Riemann manifolds

22/09/2014. Speaker: Yinon Spinka

Title: Phase structure of the loop O(n) model for large n

15/09/2014. Speaker: Pierre-Louis Giscard

Title: Of Walks and Graphs 

10/06/2014. Speaker: Ariel Yadin

Title: A Converse of Kleiner's Theorem for Linear Groups

02/06/2014. Speaker: Felix Guenther

Title: Discrete complex analysis - the medial graph approach

26/05/2014. Speaker: Slava Rychkov

Title: Conformal symmetry of critical fluctuations in three dimensions

23/05/2014. Speaker: Robin Pemantle

Title: Hexahedron recurrence, determinants and double dimer configurations

15/05/2014. Speaker: Ivan Corwin

Title: Integrable probability: beyond the Gaussian universality class

12/05/2014. Speaker: Ivan Corwin

Title: Spectral theory of ASEP, XXZ and the q-Hahn Boson process

03/03/2014. Speaker: Mikhail Katsnelson

Title: TITLE

28/02/2014. Speaker: Matan Harel

Title: The Localization Phase Transition in Random Geometric Graphs with Too Many Edges 

16/12/2013. Speaker: Alexandre Boritchev (Unige)

Title: The randomly forced 1D Burgers equation: stationary measure and turbulence.

25/11/2013. Speaker: Igor Krichever

Title: Real normalized differentials and their applications

18/11/2013. Speaker: Mahel Afif Younan (Unige)

Title: topological glasses 04.11.2013: Séminaire Lyon-Genève (voir page web)

11/11/2013. Speaker: Yves Le Jan (Paris 11)

Title: Amas de boucles markoviennes

28/10/2013. Speaker: Noam Berger (Technische Université de Munich)

Title: Local limit theorem for ballistic random walk in random environments.

28/10/2013. Speaker: John Cardy (Oxford)

Title: Lattice Stress Tensor and Conformal Ward Identities

21/10/2013. Speaker: Jean Bertoin (university of Zurich)

Title: The cut-tree of large recursive trees.

14/10/2013. Speaker: Nicolas Curien (Paris 6)

Title: On the conformal structure of random triangulations

7/10/2013. Speaker: Yacine Ikhlef (LPTHE, Université Pierre et Marie Curie/CNRS)

Title: Discrete parafermions and quantum-group symmetries

30/9/2013. Speaker: Nick Beaton

Title: Solvable models of self-avoiding walks

23/9/2013. Speaker: Vincent Vargas (CEREMADE)

Title: Complex Gaussian multiplicative chaos

19/9/2013. Speaker: Nikolai Makarov

Title: Dynamics of the Schwarz reflection

16/9/2013. Speaker: Rémi Rhodes (CEREMADE)

Title: Gaussian multiplicative chaos at criticality

9/9/2013. Speaker: Martin Hairer (Warwick)

Title: Dynamics near criticality

29/8/2013. Speaker: Scott Sheffield (MIT)

Title: QLE 

16/5/2013. Speaker: Alexandre Pouget (UNIGE)

Title: Neural computation as probabilistic inference

13/5/2013. Speaker: Laure Dumaz (ENS ulm)

Title: Some properties of the "true self repelling motion"

7/5/2013. Speaker: Omer Angel (UBC)

Title: 1 dimensional DLA

25/3/2013. Speaker: Juan Rivera-Letelier (Pontificia Universidad Catolica de Chile)

Title: Low-temperature phase transitions in the quadratic family

18/3/2013. Speaker: Sacha Glazman (Université de Genève)

Title: Connective constant for a weighted self-avoiding walk on~Z

11/3/2013. Speaker: Gaetan Borot (Université de Genève)

Title: All order asymptotics of beta ensembles in the multi-cut regime

28/2/2013. Speaker: Yuri Kifer (Hebrew University)

Title: Poisson and compound Poisson approximations in conventional and nonconventional setups

20/2/2013. Speaker: Piotr Milos (Warsaw)

Title: Delocalisation of the two-dimensional Lipschitz model 

17/12/2012. Speaker: Thierry Levy (Paris UPMC)

Title: The master field on the plane

10/12/2012. Speaker: Anthony Mays (Melbourne)

Title: A geometrical triumvirate of (non-Hermitian) random matrices

29/11/2012. Speaker: Jason Miller (MIT)

Title: Reversibility of SLE for kappa in (4,8)

26/11/2012. Speaker: Laurent Tournier (Université Paris XIII)

Title: Directional transience of oriented-edge reinforced random walks on Z^d

22/11/2012. Speaker: Hao Wu (Orsay)

Title: Conformally Invariant Growing Mechanism in CLE_4 and Couplings between GFF and CLE_4

19/11/2012. Speaker: Alex Fribergh (Toulouse)

Title: On the monotonicity of the speed of biaised random walk on a Galton-Watson tree without leaves

13/11/2012. Speaker: Nathanael Berestycki (Cambridge)

Title: A new approach to the Brownian web

5/11/2012. Speaker: Yair Hartman (Weizmann Institute)

Title: Random walks on groups and recurrent subgroups

29/10/2012. Speaker: Pierre-François Rodriguez (ETH)

Title: On the level-set percolation for the Gaussian free field

15/10/2012. Speaker: Béatrice de Tillière (UPMC)

Title: Loops in the XOR Ising model

8/10/2012. Speaker: Christophe Sabot (Université Lyon 1)

Title: Edge reinforced random walks, Vertex reinforced jump process, and the SuSy hyperbolic sigma model.

1/10/2012. Speaker: Amandine Veber (Ecole Polytechnique)

Title: Evolution of the interface between types in a spatially extended population

24/9/2012. Speaker: Igor Kortchemski (Orsay)

Title: Random trees conditioned to be large

17/9/2012. Speaker: Gordon Slade (UBC)

Title: Growth constants for lattice trees and lattice animals in high dimensions 

30/5/2012. Speaker: Jeremie Bettinelli (Orsay)

Title: Scaling limit of arbitrary genus random maps

22/5/2012. Speaker: Alain-Sol Sznitman (ETH)

Title: On Gaussian free fields and random interlacements

14/5/2012. Speaker: Rémi Peyre (Nancy)

Title: McKean–Vlasov Metastability

7/5/2012. Speaker: Pietro Caputo (Roma Tre)

Title: On the spectrum of random Markov matrices

2/5/2012. Speaker: Serge Richard (Université de Lyon)

Title: Théorèmes d'indice en théorie de la diffusion

26/4/2012. Speaker: Remco van Der Hofstad (Eindhoven University of technology)

Title: The survival probability and r-point functions in high dimensions

25/4/2012. Speaker: Ron Peled (Tel Aviv University)

Title: Probabilistic existence of rigid combinatorial structures

23/4/2012. Speaker: Nicolas Curien (ENS Ulm)

Title: relation between the intersection property and reccurence

16/4/2012. Speaker: Emanuel Millman (Technion)

Title: Transference Principles for Log-Sobolev and Spectral-Gap Inequalities with Applications to Conservative Spin Systems

2/4/2012. Speaker: Pierre Nolin (ETH)

Title: A modified frozen percolation process on the binary tree and on the square lattice

19/3/2012. Speaker: Raphael Cerf (Orsay)

Title: Nucleation and growth for the Ising model in d dimensions at very low temperatures

12/3/2012. Speaker: Marc Wouts (Paris XIII)

Title: Glauber dynamics for the quantum Ising model on a tree

7/3/2012. Speaker: Cyrille Lucas (Paris X)

Title: Internal Diffusion Limited Aggregation, from the centered to the drifted case

21/2/2012. Speaker: Ross Pinsky (Technion)

Title: Probabilistic and Combinatorial Aspects of the Card-Cyclic to Random Insertion Shuffle

20/2/2012. Speaker: Martin Hairer (Warwick)

Title: Solving the KPZ equation 

6/12/2011. Speaker: Vladislav Vysotsky

Title: Persistence of integrated random walks

9/12/2011. Speaker: Laszlo Erdos (Munich)

Title: The local version of Wigner's semicircle law and Dyson's Brownian motion

12/12/2011. Speaker: Gady Kozma (Weizman institute)

Title: Harmonic maps on Cayley graphs

13/12/2011. Speaker: Vladas Sidoravicius (IMPA)

Title: Stability of the waiter

19/12/2011. Speaker: Konstantin Izyourov (Université de Genève)

Title: soutenance de thèse

20/12/2011. Speaker: Ilya Gruzberg (University of Chicago)

Title: Quantum Hall transitions and conformal restriction

5/12/2011. Speaker: Ioan Manulescu (Cambridge)

Title: Bond Percolation on Isoradial Graphs

28/11/2011. Speaker: Thierry Bodineau (ENS Paris)

Title: Transition de phases pour des dynamiques avec contraintes

22/11/2011. Speaker: Mireille Bousquet-Mélou (university Bordeaux 1)

Title: The Potts model on planar maps

16/11/2011. Speaker: Nicolas Monod (EPFL)

Title: Littlewood and large forests

14/11/2011. Speaker: Damien Simon (UPCM)

Title: Some recent algebraic and probabilistic results on the asymmetric exclusion process with reservoirs

11/11/2011. Speaker: Wendelin Werner (Orsay)

Title: Describing surface fluctuations

3/11/2011. Speaker: Michael Monastyrsky (ITEP and EPFL)

Title: Kramers-Wannier Duality, Old and New Results

31/10/2011. Speaker: Paul Fendley (University of Virginia)

Title: Discrete Holomorphicity from Topology

24/10/2011. Speaker: Adrien Joseph (ENS Cachan)

Title: The component sizes of a critical random graph

17/10/2011. Speaker: Fabio Martinelli (University Roma tre)

Title: Sharp mixing time bounds for sampling random surfaces

13/10/2011. Speaker: Gregory Falkovich (Weizman)

Title: Broken and emerging symmetries of the turbulent state

10/10/2011. Speaker: Jérémie Bouttier (Institut de Physique Théorique)

Title: Des boucles sur les cartes aléatoires 

4/4/2011. Speaker: Bertrand Eynard (DSM-CEA/Saclay)

Title: Exact results for statistical models on random lattices

11/2/2011. Speaker: Nicolas Curien (Ecole normale supérieure)

Title: A view from infinity of the uniform infinite planar quadrangulation

22/11/2010. Speaker: Kostantin Izyurov (Université de Genève)

Title: Holomorphic spinor observables in the Ising model

17/11/2010. Speaker: Vladas Sidoravicius (IMPA)

Title: Abundance of maximal paths

15/11/2010. Speaker: Sacha Friedli (Universidade Federal de Minas Gerais)

Title: Singularités essentielles des potentiels thermodynamiques

8/11/2010. Speaker: Hubert Lacoin (Universita di Roma tre)

Title: Polymères dirigées en milieu aléatoire: diffusivité ou localisation

25/10/2010. Speaker: David Cimasoni (Université de Genève)

Title: La formule de Kac-Ward généralisée

19/10/2010. Speaker: Jan De Gier (University of Melbourne)

Title: Exact finite size percolation operator between boundaries of a lattice strip

4/10/2010. Speaker: Hugo Duminil-Copin (UNIGE)

Title: Self-avoiding walks on the hexagonal lattice 

Mardi 6 juillet, 2010 : Mohammad Rajabpour (INFN, Turin)

Ashkin-Teller model on the iso-radial graphs

Lundi 14 juin, 2010 : Ilya Gruzberg (Chicago University)

Stochastic Loewner chains for DLA-like growth

Jeudi 10 juin, 2010, à 16h15, en salle 17 : Vladimir Mangazeev (ANU, Canberra)

Quantum geometry of 3D lattices

Mercredi 2 juin, 2010, à 13h15 en salle 623 : Eldad Bettelheim (Hebrew University of Jerusalem)

Tau functions and differential equations for the real time evolution of free fermions

Mercredi 19 mai, 2010, 13h15, salle 623 : Jason Miller (Stanford)

Universality for SLE(4)

Lundi 17 mai 2010: Nikolai Makarov (Caltech)

Radial explorer and its two conformally invariant theories

Vendredi 14 mai 2010, 13 h 25, salle 623 : Hugo Duminil-Copin (UNIGE)

Groupe de travail sur RSW

Lundi 10 mai 2010: Rinat Kashaev (UNIGE)

Informal seminar about the colored Jones polynomial

Vendredi 8 mai 2010: Yacine Ikhlef (UNIGE)

Groupe de travail sur le modèle O(n)

Lundi 19 avril 2010: Nicholas Varopoulos (Unige) 

Green's function on quasidisks

Lundi 12 avril 2010 : Ilia Binder (Toronto) 

Efficient computation of harmonic measure and boundary geometry

Mercredi 24 mars 2010 : B. Doyon (King's College London)

Calculus on infinite-dimensional manifolds, conformal field theory, and its probabilistic descriptions

Lundi 22 mars 2010 : N. Curien (ENS)

Recursive triangulations and fragmentation theory

Lundi 15 mars 2010 : P. Nolin (Courant Institute)

Monochromatic arm exponents for 2D percolation 

Mercredi 3 mars 2010 : G. Miermont (Université Paris-Sud)

Scaling limits of random planar maps with large faces

Jeudi 4 février 2010 : N. Th. Varopoulos

Random walks in complex domains

Lundi 14 décembre 2009 : Rémi Peyre (ENS Lyon)

Variables aléatoires partiellement indépendantes : une approche hilbertienne

Vendredi 11 décembre 2009, 13h30 : Anton Alekseev (UNIGE)

Séminaire informel sur WZW, KZ et SLE

Lundi 7 décembre 2009 : Bernard Nienhuis

Critical percolation and qKZ equations

Mercredi 18 novembre 2009 : Kari Astala (Helsinki)

Informal seminar on random weldings and quasiconformal maps 

Lundi 16 novembre 2009: Antti Kupiainen (Helsinki)

Random Weldings

Jeudi 12 novembre 2009, 16h15, salle 17 : Phillipe Di Francesco (CEA Saclay)

Integrable Combinatorics

Vendredis 27 novembre et 4 décembre 2009 : Dmitry Beliaev (UNIGE)

On a theorem of Tsirelson

Lundi 30 novembre 2009 : Alain-Sol Sznitman (ETHZ)

Disconnection of discrete cylinders and random interlacements

Mercredi 11 novembre 2009 : séminaire informel

29 septembre et 15 octobre 2009 : Thierry Lévy (UNIGE) 

Mesure et action de Yang-Mills en deux dimensions

(séminaire Groupes de Lie et espaces de modules)

Lundi 28 septembre 2009 : Christophe Garban (ENS Lyon)

Near-critical and dynamical percolation scaling limits

Lundi 21 septembre 2009 : Vincent Beffara (ENS Lyon)

Slow progress on the slow bond problem

Vendredi 5 juin 2009, 15h15 : Nikolai Makarov (Caltech)

Random normal matrices

Lundi 18 mai 2009 : Antti Kemppainen (Helsinki)

Describing scaling limits of random planar curves by SLEs

Lundi 28 avril 2009 : Jürgen Angst (Strasbourg)

Mouvement brownien dans le cadre de la théorie de la relativité

Lundi 6 avril 2009 : Nicolas Orantin (CERN)

Énumération de cartes et matrices aléatoires

Lundi 30 mars 2009 : Adam Timar (Bonn)

Equivariant colorings of random planar graphs

Mardi 24 mars 2009, 14h00, salle 17 : Christian Mercat (Montpellier)

Surfaces de Riemann discrètes et modèle d'Ising

Lundi 9 mars 2009 : Nicolas Monod (EPFL)

Littlewood and Large Forests

Vendredi 6 mars 2009, 15h, salle 17 : Bernard Sapoval (École polytechnique et ENS Cachan)

Physical problems related to gradient and extreme gradient percolation

Lundi 15 décembre 2008 : Béatrice de Tilière (UNINE)

Lundi 24 novembre 2008 : Sacha Friedli (Belo Horizonte)

Chaînes à longue portée et le mécanisme de Bramson-Kalikow

Lundi 17 novembre 2008 : Istvan Prause

Harmonic measure and quasiconformal mappings

Lundi 10 novembre 2008 : Yacine Ikhlef

Observables holomorphes sur réseau et modèles de boucles intégrables

Lundi 3 novembre 2008 : David Ridout (DESY theory group, Hamburg)

Critical Percolation as a CFT (with a view to SLE)

Jeudi 30 octobre 2008 (13h, salle 623) : Viviane Baladi (ENS Paris)

Espaces de Banach adaptés aux dynamiques hyperboliques avec singularités et aux billards

Lundi 20 octobre 2008 : Cédric Boutillier (Université Paris VI et UniNE)

Scaling limits for random skew plane partitions with a piecewise periodic back wall

Jeudi 16 octobre 2008 (13h, salle 623) : David Cimasoni (ETHZ)

The dimer model, discrete spin structures and discrete d-bar operators

Lundi 6 octobre 2008 : Olivier Bernardi (Université Paris-Sud)

Comptage des cartes coloriées

Lundi 29 septembre 2008 : Bertrand Eynard (SPhT, CEA - Saclay)

Plancherel measure on partitions, matrix models and Gromov-Witten theory

Lundi 22 septembre 2008 : Gregory Miermont (Université Paris-Sud et ENS Paris)

Propriétés géométriques des grandes cartes aléatoires