The GPP Seminar is the UCL-KULeuven seminar in the framework of the Interuniversity Attraction Pole (IAP)
"Nonlinear systems, stochastic processes, and statistical mechanics" (NOSY). It is alternately held in the mathematics-physics building at UCL (Chemin du Cyclotron 2, Louvain-la-Neuve) or in the mathematics building (Celestijnenlaan 200B, Heverlee) at the KULeuven.
Organizers : Pierre Bieliavsky (UCL), Jean Bricmont (UCL), Tom Claeys (UCL), Luc Haine (UCL), Arno Kuijlaars (KULeuven), Philippe Ruelle (UCL), Walter Van Assche (KULeuven), Pierre van Moerbeke (UCL).
Forthcoming seminars
Thursday 22/3 - 16:15 [room FYMA -CYCL b 328, UCL]
Alfredo Deaño (Universidad Carlos III de Madrid)
"Partition function and free energy in the cubic random matrix model"
Abstract | We consider a unitary random matrix model with weight function e^{-NV(z)}, where V(z)=z^2/2-uz^3 and u is a real positive parameter. One feature of this model is that the partition function has to be defined in the complex plane. For u smaller than a critical value u_c, the free energy admits an asymptotic expansion in powers of N^{-2}. The first two terms of this topological expansion are known from the work of Brézin, Itzykson, Parisi, and Zuber (Commun. Math. Phys. 59 (1978), 35-51), and can be written in terms of classical hypergeometric functions. Near the critical value, a double scaling limit leads to an asymptotic approximation in terms of a particular solution of Painlevé I. Our results are obtained by a Riemann--Hilbert analysis of the corresponding family of orthogonal polynomials in the complex plane, together with the string equations for the associated recurrence coefficients. (joint work with Pavel M. Bleher, Indiana University-Purdue University Indianapolis, USA)
Talks 2012
Friday 9/3 - 16h15 [room FYMA -CYCL b 328, UCL]
Stéphane Korvers (UCL)
"Étude des aspects géométriques et analytiques d’une extension d’un processus de quantification par déformation de l’espace symétrique symplectique SU(1,1)/U(1)"
Abstract | Dans « The Deformation Quantizations of the Hyperbolic Plane » (P. Bieliavsky, S. Detournay, Ph. Spindel ; Communications in MathematicalPhysics ; Springer-Verlag 2008) les auteurs montrent qu'une contraction de courbure du plan hyperbolique livre une surface symétrique symplectique dont le groupe de transvections est isomorphe au groupe de Poincaré en dimension deux. Ils montrent également que de ce processus de contraction émerge un opérateur différentiel d'ordre deux dont certaines solutions de l'évolution définissent des opérateurs de convolution qui entrelacent la théorie des déformations (produits-étoile) au niveau contracté avec celle du plan hyperbolique. Cet exposé consistera en un bref aperçu de la généralisation de cette construction au cas de l'espace symétrique symplectique SU(1,n)/U(n) et en l’analyse des résultats annexes obtenus à partir d’une étude géométrique de l’opérateur différentiel d'ordre deux dans le cas du plan hyperbolique. [±]
Friday 24/2 - 16h15 [room FYMA -CYCL b 328, UCL]
Mark Adler (Brandeis University)
"RMT minors and percolation Theory "
Thursday 9/02 (16:15) [room FYMA -CYCL b 328, UCL]
Daniela Rosca (Univ. Techn. Cluj, Roumania)
"Area preserving maps, uniform grids, and the associated wavelet analysis"
Abstract | We give three different methods for constructing some area preserving bijections. Then we apply these bijections to uniform rectangular grids and we obtain uniform grids on the disc, elliptic domains and surfaces of revolution. Combined with the Lambert azimuthal projection, our new maps can be used to obtain new uniform and refinable (UR) grids on the sphere, starting from (UR) grids on rectangles. At the end we show how a given wavelet analysis of R^2 can be transported to surfaces of revolution.
Thursday 26/01 (16:15) [ room FYMA -CYCL b 328, UCL]
Jean-Pierre Antoine (UCL)
"Partial inner product spaces, a unifying concept in functional analysis (2)"
Abstract | Many families of function spaces play a central role in analysis, in particular in signal processing (e.g. wavelet or Gabor analysis). Such are Lp spaces, Besov spaces, amalgam spaces or modulation spaces. In all such cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators. In this context, it is often said that such families should be taken as a whole and operators, bases, frames on them should be defined globally, for the whole family, instead of individual spaces. It turns out that all these space families are scales or lattices of Banach spaces, and as such they are special cases of partial inner product spaces (pip-spaces). These objects, which may often be seen as an alternative to the theory of tempered distributions, have been studied systematically in many papers and are now the subject of a recent monograph [1]. The interesting fact is precisely that they allow a global definition of operators, and various operator classes on them have been defined. In these talks, we shall give an overview of pip-spaces and operators on them, illustrating the results by space families of interest in mathematical physics and signal analysis. [1] J-P. Antoine and C. Trapani, Partial Inner Product Spaces — Theory and Applications; Lecture Notes in Mathematics, vol. 1986, Springer-Verlag, Berlin, Heidelberg, 2009... [±]
Talks 2011
Thursday 22/12 (16h 15) [room FYMA - CYCL b328, UCL]
Pierre van Moerbeke (UCL)
"The tacnode process (2)"
Thursday 15/12 (16h 15) [room FYMA - CYCL b 328, UCL]
Jean-Pierre Antoine (UCL)
"Partial inner product spaces, a unifying concept in functional analysis (2)"
Thursday 08/12 (14h30) [room FYMA - CYCL b 328, UCL]
Jean-Pierre Antoine (UCL)
"Partial inner product spaces, a unifying concept in functional analysis (1)"
Abstract: Many families of function spaces play a central role in analysis, in particular in signal processing (e.g. wavelet or Gabor analysis). Such are Lp spaces, Besov spaces, amalgam spaces or modulation spaces. In all such cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators. In this context, it is often said that such families should be taken as a whole and operators, bases, frames on them should be defined globally, for the whole family, instead of individual spaces. It turns out that all these space families are scales or lattices of Banach spaces, and as such they are special cases of partial inner product spaces (pip-spaces). These objects, which may often be seen as an alternative to the theory of tempered distributions, have been studied systematically in many papers and are now the subject of a recent monograph [1]. The interesting fact is precisely that they allow a global definition of operators, and various operator classes on them have been defined. In these talks, we shall give an overview of pip-spaces and operators on them, illustrating the results by space families of interest in mathematical physics and signal analysis.
[1] J-P. Antoine and C. Trapani, Partial Inner Product Spaces — Theory and Applications; Lecture Notes in Mathematics, vol. 1986, Springer-Verlag, Berlin, Heidelberg, 2009
Thursday 01/12 (16h 15) [room FYMA - CYCL b 328, UCL]
Pierre van Moerbeke (UCL)
"The tacnode process (1)"
Thursday 24/11 (16h 15) [room FYMA - CYCL b 328, UCL]
Tom Claeys (UCL)
"Random matrix models with equi-distant external source"
Abstract: I will discuss random matrix ensembles with a full rank external source. The eigenvalues of the external source are equi-spaced on an interval. I will set up a Riemann-Hilbert problem for the associated multiple orthogonal polynomials and explain how an asymptotic analysis for this problem can be performed. The limiting mean eigenvalue distribution of the model will be described in terms of an equilibrium problem, and bulk and edge universality will be discussed. This is based on joint work in progress with Dong Wang.
Thursday 10/11 (15h 30) [room FYMA - CYCL b 328, UCL]
Jean-Pierre Gazeau (Paris 7)
"Coherent states and related quantizations for unbounded motions"
Abstract: We present two different methods of construction of coherent states for unbounded motions. The first one adapts the Malkin-Manko approach to such systems and is illustrated by the example of a charged particle in an electric field. The second approach associates to a conservative mechanical system with observed continuous energy spectrum families of corresponding ``pseudo-action-angle'' coherent states. These states are constructed in view to provide a quantization scheme consistent with this continuous range of experimental energies. The formalism is a natural extension of the Bohr-Sommerfeld rule and an alternative to the canonical quantization. Some semi-classical behaviors of such states will be shown.
Thursday 30/6 (16:00) [romm b328]
Galina Filipuk (University of Warsaw)
"Orthogonal polynomials and Painleve equations: Charlier, Meixner and Laguerre cases Location"
Thursday 12/5 (16h15) [b328]
Jean-Pierre Antoine
"Frames and semi-frames"
Thursday 5/5 (16h15) [b328]
Georg Rieckh (Vienna)
"Frame Representation of Boundary Integral Operators"
Thursday 28/4 (16h15) [b328]
Abey Lopez Garcia (K.U.Leuven)
"Some discrete minimal energy problems: asymptotics of Leja and Fekete points"
Friday 08/04 (16h 15) [room FYMA - CYCL b328, UCL]
Igor Krasovsky (Brunel University London)
"Asymptotics of Toeplitz determinants"
Thursday 07/04 (15h00) [Fyma b328, UCL]
Brian Rider (University of Colorado)
"Some solvable two-charge models"
Thursday 31/03 (15h20) [Room B02.18, Celestijnenlaan 200B, KULeuven]
Dong Wang (UCL, on leave from University of Michigan)
"Random matrix models with spiked external source"
Abstract: In this talk I will show results on random matrix models with spiked (i.e., finite rank) external source. We discuss orthogonal, symplectic and unitary ensembles, and for orthogonal and symplectic ensembles we consider mostly the rank 1 case. Part of the talk is based on joint work with Jinho Baik.
Thursday 10/3 (16h) [FyMa, b328]
Lun Zhang (K.U.Leuven)
"Large n limit of non-intersecting squared Bessel pahts "
Friday 4/3 (16h) [FyMa, b328]
Lise Ponselet (UCL)
"Transitions de phase des automates cellulaires probabilistes"
Thursday 24/2 (16h) [FyMa, b328]
Jean Pierre Gazeau (Paris 7)
"Les quantifications canonique et par états cohérents sont-elles physiquement équivalentes?"
Resumé: Il a été récemment soutenu (Kastrup, 2006) que la quantification canonique est la seule permettant d'expliquer l'observation, remontant aux premières années de la mécanique quantique, de déplacements des raies dans les spectres de vibrations pour des molécules diatomiques isotopiques. Je montrerai que la quantification par états cohérents est une alternative parfaitement valide quant à ses prédictions sur les spectres en question.
Talks 2010
Thursday 16/12/10 (14:30) [UCL, room FYMA - CYCL b328]
Jean Bricmont (UCL)
"The Fourier law (2)"
Abstract (Second of two talks)
In this second talk, I will describe some specific microscopic models where one tries to derive Fourier's law, mention some results that have been obtained, and explain the role that "chaotic" dynamical systems might play.
Thursday 09/12/10 (14:30) [UCL, room FYMA - CYCL b328]
Jean Bricmont (UCL)
"The Fourier law (1)"
Abstract (First of two talks)
Fourier's law on heat conduction is one of the most basic and simplest of the macroscopic physical laws. One of the goals of statistical mechanics is to derive such laws from the microscopic mechanical ones, but this has turned out to be extremely hard.
In the first talk, I will explain the general framework in which such a derivation might be done, and why, although Fourier's law leads to irreversible behaviour, it is not a priori impossible to derive it from reversible microscopic ones; nevertheless, because of this irreversible behaviour, this derivation can only be done, if at all, under certain conditions that will be explained.
Thursday 02/12/10 (14:30) [UCL, room FYMA - CYCL b328]
Philippe Ruelle (UCL)
"From statistical models to conformal field theories (3)"
Thursday 25/11/10 (14:30) [UCL, room FYMA - CYCL b328]
Philippe Ruelle (UCL)
"From statistical models to conformal field theories (2)"
Thursday 18/11/10 (14:30) [UCL, room FYMA - CYCL b328]
Philippe Ruelle (UCL)
"From statistical models to conformal field theories (1)"
Abstract (3 talks, the first one will be an introductory talk)
For the last 25 years, conformal theory has arguably been among the most productive factory of exact -but non rigorous- results in physics and mathematics. It was originally conceived to describe the critical properties of statistical models (f.i. the Ising model), and has indeed led to spectacular progress in the understanding of critical universality classes, especially in two dimensions. The series of talks is meant to be an introduction to the ideas underlying the description of critical models by conformal theories. I will try to give a feeling for the methodology of conformal theories and for some of their technical aspects.
Thursday 10/11/10 (14:30) [UCL, room FYMA - CYCL b328]
Tom Claeys (UCL)
"Asymptotics for the Korteweg-de Vries equation and perturbations using Riemann-Hilbert method (3)"
Thursday 28/10/10 (14:30) [UCL, room FYMA - CYCL b328]
Tom Claeys (UCL)
"Asymptotics for the Korteweg-de Vries equation and perturbations using Riemann-Hilbert method (2)"
Thursday 14/10/10 (14:30) [UCL, room FYMA - CYCL b328]
Tom Claeys (UCL)
"Asymptotics for the Korteweg-de Vries equation and perturbations using Riemann-Hilbert method (1)"
Abstract (3 talks, the first one will be an introductory talk)
Small dispersion asymptotics for solutions to the Korteweg-de Vries equation can be obtained using Riemann-Hilbert problems. In critical regimes, this leads to asymptotic expansions in terms of Painlevé transcendents. I will give an overview of this procedure, and I will discuss some obstacles that occur when considering non-integrable perturbations of the Korteweg-de Vries equation. This is based on joint work with Tamara Grava, and on joint work in progress with Tamara Grava and Ken McLaughlin.
"IAP Workshop: Integrable Systems 2"
Wednesday February 10, 10:00 - 16:30
Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, room CYCL 01.
- 10:00 - 11:00
Pablo Manuel Roman (KULeuven)
Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths
- 11:15 - 11:45
Didier Vanderstichelen (UCLouvain)
A centerless representation of the Virasoro algebra associated with the unitary circular ensemble
- 12:00 - 12:30
Gilles Regniers (UGent)
On Wigner quantization of H=xp, representations of osp(1|2) and orthogonal polynomials
- 14:15 - 15:15
Tom Claeys (Université Lille 1)
Critical asymptotics for Toeplitz determinants
- 15:30 - 16:30
Eric Nordenstam (UCLouvain)
Dynamics on Interlaced Particles
Talks 2009
Wednesday, 04/11/09 (13:30) [KULeuven, Room B.02.18, Celestijnenlaan 200B, Leuven]
Eric NORDENSTAM (UCLouvain)
"Determinantal point processes from the perspective of Alexei Borodin"
"Workshop: Integrable Systems"
Wednesday May 27 14.30-17.10, Celestijnenlaan 200B, Leuven, room B.00.16.
- 14:30-15:10
Walter Van Assche:
Introduction to multiple orthogonal polynomials
- 15:30-16:10
Gilles Regniers and Joris Van der Jeugt:
Analytically solvable quantum Hamiltonians and relations to orthogonal polynomials
- 16:30-17:10
Mattia Cafasso:
Toda-type equations extended to the case of mixed multiple orthogonal polynomials
Thursday, 30/04/09 (16:30) [UCL, room FYMA - CYCL b328]
Marco Bertola (Concordia University, Montreal)
"Riemann--Hilbert problems: Malgrange, Schlesinger and Sato"
Abstract : Given any (sufficiently well-behaved) family of Remann--Hilbert problems where the jump matrices depend arbitrarily on deformation parameters, we can construct a one-form $\Omega$ on the deformation space (Malgrange's differential). Such a one--form has a pole where the deformation family meets the Malgrange Theta divisor, namely, the set of unsolvable RHP. The differential $\Omega$ fails to be closed in general, but when it does the formula $\tau := {\rm e}^{\int \Omega}$ defines locally a function that vanishes precisely on $\Theta$.
Friday 24/04/09 (11:00) [UCL, room FYMA - CYCL b328]
Raphaël LEFEVERE (Université Denis Diderot, Paris 7)
"Hot scatterers and tracers for the transfer of heat in collisional dynamics"
Abstract : We consider two models for the transport heat in systems described by local collisional dynamics. The dynamics of those models consist of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed temperatures. Those models have the structure of Markov renewal processes whose large deviations and ergodic properties are studied in details. When the set of temperatures is fixed by the condition that in average, no energy is exchanged between the scatterers and the system, two behaviours may occur. When the tracer particles are allowed to travel freely through the whole array of scatterers, the temperature profile is linear. If the particles are locked in between scatterers, the temperature profile becomes nonlinear. In both cases, Fourier law holds. Joint work with L. Zambotti.... [±]
Location | Fyma seminar room, b328, Louvain-la-Neuve
Friday 13/03/09 (11:00) [UCL, room FYMA - CYCL b328]
Yukitaka Ishimoto (Okayama Institute for Quantum Physics)
"Solving infinite Kolam in knot theory"
Abstract: In south India, many ladies draw a certain type of complicated line patterns every morning in front of their houses, with white rice powder on the ground. The class of pattern is drawn around a grid pattern of dots so that the lines minimally encircle each dot, which is called line "Kolam" pattern in Tamil.
Among them, one-line drawings or the "infinite Kolam" have some special meaning not only ethnologically but also mathematically. For example, we can address the following simple question: How many can we draw such patterns/diagrams for a given grid pattern of dots?
One may think that the problem is NP-hard alike: almost all cases should be examined for the solution. However, it is certainly not. In this talk, we focus on the knot-theoretical description of the infinite Kolam and show how to find the solution, which inevitably gives a sketch of the proof for the statement "infinite Kolam is not NP hard." Further discussions on Kolam may also be given.
Thursday 12/03/09 (16:30) [UCL, room FYMA - CYCL b328]
Eric NORDENSTAM (KTH - Stockholm)
"The shuffling algorithm and the Aztec diamond"
Abstract: The shuffling algorithm, introduced by Elkies et al., for sampling tilings of the Aztec diamond uniformly at random can be seen as a certain dynamics on a set of interacting particles. This is in some sense a discretization of a model of interlacing Brownian motions studied by Warren. As an application of these results, I will sketch a new proof of the fact that, in suitable scaling limit of large Aztec diamonds, one can recover the distribution of the eigenvalues of a GUE matrix and its principal minors.
Thursday 26/02/09 (10:45) [UCL, FYMA - CYCL b328]
Carlangelo LIVERANI (Université de Rome Tor Vergata)
"Toward the derivation of the Fourier law from an Hamiltonian model"
Abstract: I will discuss a program to obtain the Fourier law (or rather the heat equation), starting from an anharmonic lattice with some amount of noise. The noise is of a fixed level and it is not directly responsible for the energy exchanges. This is a joint work with Stefano Olla.
Thursday 12/02/09 (14:00) [UCL, FYMA - CYCL b328]
Christian HAGENDORF (Ecole Normale Supérieure, Paris)
"Loop erased random walks and SLE"
Talks 2008
Tuesday 02/09/2008 (15:00) [KULeuven, room 02.18 Celestijnenlaan 200B]
Pablo ROMAN (Cordoba, Argentina)
"Matrix valued spherical functions associated to the complex hyperbolic plane and the hypergeometric operator "
Thursday 22/05/2008 (16:30) [UCL, Louvain-la-Neuve, Chemin du Cyclotron 2, CYCL 10]
Patrik FERRARI (Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin)
"Anisotropic growth of random surfaces in 2+1 dimensions"
Friday 25/04/2008 (16:00) [KULeuven, Celestijnenlaan 200B, Leuven (Heverlee), Room B.02.18]
Alexander Its (IUPUI, Indianapolis, USA)
"Global asymptotic analysis of the Painlevé transcendents"
Wednesday 23/04/2008 (10:30) [UCL, Louvain-la-Neuve, Chemin du Cyclotron 2, CYCL 10]
Kurt Johansson (KTH-Stockholm)
"Universality results in random matrices"
Friday 11th April at 14:00 - [Location : CYCL08 (Louvain La Neuve)]
Micha Pevzner (Universite de Champagne-Ardennes REIMS)
"Crochets de Rankin-Cohen et Quantification des espaces symétriques"
Thursday 3rd April at 16:00 - [Location : room CYCL08 at Louvain-la-Neuve, chemin du cyclotron]
Steven Delvaux (KULeuven)
"A phase transition for non-intersecting Brownian motions, and the Painlevé II equation"
Talks 2007
Thursday 20/12/07 (16h15) [Heverlee, KULeuven, Celestijnenlaan 200B, salle 200B 01.18]
Mark Adler (Brandeis University)
The Pearcey Process Revisited - An Attempt to Break Symmetry
Thursday 06/12/2007 (16h15) [UCL, Louvain-la-Neuve, Chemin du Cyclotron 2, salle CYCL b328]
Milton Jara (Phys. UCL)
An introduction to the tagged particle problem
Thursday 22/11/07 (16h 15) [UCL, Louvain-la-Neuve, Chemin du Cyclotron 2, salle CYCL b328]
Maurice Duits [KULeuven-Math]
Asymptotics of certain biorthogonal polynomials associated to a two-matrix model
Thursday 08/11/2007 (16h15) [Heverlee, KULeuven, Celestijnenlaan 200S, salle 200S 00.04]
Nicolas Orantin (Math. UCL)
Symplectic invariants and loop equations
Thursday 25/10/2007 (16h15) [Lieu: Heverlee, KULeuven, Celestijnenlaan 200C, salle 200C 01.02]
Nicolas Orantin (Math. UCL)
Formal matrix models and combinatorics of maps
Thursday 11/10/2007 (16h15) [LLN - CYCL 10]
Ivar Lyberg (Phys. UCL)
Form factor expansion of correlation functions of the two dimensional Ising lattice
Friday 28/09/2007 (16h15) [ LLN - CYCL 02]
Arno Kuijlaars (Math. KULeuven)
Non-intersecting squared Bessel processes
Wednesday 19/09/2007 (16h30) [Heverlee, KULeuven, Celestijnenlaan 200 B, room 200B.02.18]
Tom Claeys (Math. KULeuven)
The "birth of a cut"-transition in random matrix ensembles
Friday 22/06/2007 (10h45) [LLN - CYCL04]
Didier Vanderstichelen (Math UCL)
Modèles combinatoires et intégrales sur le groupe unitaire
Friday 23/03/2007 (10h45) [LLN - CYCL04]
Jean Bricmont (Physique UCL)
Une introduction "pédestre" au groupe de renormalisation (2ème partie)
Friday 09/03/2007 (10h 45) [LLN - CYCL04]
Jean Bricmont (Physique UCL)
Une introduction "pédestre" au groupe de renormalisation (1ère partie)
Friday 23/02/2007 (10h 45) [LLN - CYCL04]
Yuri Berest (Cornell and IHES)
Ideals of rings of differential operators on smooth curves
Talks 2006
Friday 08/12/2006 (10h45) [LLN - CYCL07]
Augustin de Maere (Phys. UCL)
Transitions de phase dans les réseaux d'applications couplées II (preuve de l'existence)
Friday 01/12/2006 (10h 45) [LLN - CYCL07]
Augustin de Maere (Phys. UCL)
Transitions de phase dans les réseaux d'applications couplées I (exposé introductif)
Friday 17/11/2006 (10h45) [LLN - CYCL07]
Jonathan Delepine (Math. UCL)
Equations aux dérivées partielles pour la distribution du spectre de modèles matriciels aléatoires
Friday 10/11/2006 (10h45) [LLN - CYCL07]
Ariane Leblanc (Math. UCL et Poitiers)
Structures de (quasi)-Poisson quadratiques et construction d'un système intégrable sur un espace de modules
Friday 03/11/2006 (10h45) [LLN - CYCL 07]
François Huveneers (Phys. UCL)
Renormalisation et problèmes de petits diviseurs
Friday 27/10/2006 (10h45) [LLN - CYCL07]
Luc Haine (Math. UCL)
Collisions dans le système de Calogero-Moser
