Talks and Conferences

To Come:

sept 2018: Strasbourg, invited talk
sept 2018: Banff, invited talk
may 2018: Leeds, UK, invited talk
june 2018: Lyon, invited talk
2nd semester 2017-2018: Master probabilité Université Paris Sud (ORsay) : Random matrices.
april 2018: IHES lectures: Topological recursion.
jan 2018: Saclay lectures: Riemann surfaces.
aug 2017: Talk at the conference in honor of J. Hurtubise, Montreal, QC, reconstructing a dispersive integrable system from the geometry of a spectral curve, using topological recursion. canceled.
july 2017: lecture at the pre-string-math conference, Hamburg, GE. Topological recursion in enumerative geometry.
june 27 2017, Nice, seminar, math department, UNICE. des asymptotiques des grandes Matrices aléatoires aux invariants en géometrie algébrique.
june 19 2017, Saclay, math-phys seminar: Topological recursion and quantization: from Eynard-Orantin to Kontsevich-Soibelman frameworks.
may 2017, Lyon
june-july 2017, IAS / Park City Mathematics Institute (PCMI) Research Program, Random Matrices, canceled
dec 9, 2016, seminar, Nantes, TBA
dec 8, 2016, Colloquium, Nantes, TBA
nov, 2016, Groupe de travail, Saclay, Integrable systems and geometry
july 4-8, 2016, AMS Von Neumann symposium, Charlotte, NC, USA, Topological Recursion and its Inﬂuence in Analysis, Geometry, and Topology,
march 2016, Vienna. canceled
feb 2016, Oberwolfach MFO workshop, Topological recursion and TQFT. canceled.
nov 2015, Colloquium Tours
nov 2015, Simons Center for Geometry and Physics, Random Matrix Theory, Integrable Systems, and Topology in Physics. canceled.
jan 2016, Thematic semester CRM Montréal, workshop on topological recursion,
fall 2015, Chaire Aisenstadt, CRM Montréal,
July 2015, Summer school Les Houches, Stochastic processes and random matrices,
june 2015, 20^th conference Itzykson, Saclay, organizer.
1-5 june 2015, Leiden, Netherlands, Geometric invariants and spectral curves,
11 may, Orsay, math department Colloquium. Topological recursion: from random matrices to geometry.
21 april 2015: IHES, seminar. CFTs, and the (quantum) geometry of integrable systems.
13 april 2015: Saclay, mathematical physics seminar. CFTs, and the (quantum) geometry of integrable systems.
13-17 april 2015: MSRI Berkeley, Dynamics on Moduli Spaces, canceled.
7-10 april 2015: Orsay, Quantum Gravity in Paris,
12 march: Nottigham, weekly seminar, canceled.
9 jan- 13 feb 2015: Saclay's lecture series, Random Matrices, Theory and applications,
26-30 january 2015, Cambridge, Newton Institute. Canceled.
2 dec 2015: Itzykson seminar, IHES,
Topological Recursion,
24-28 november 2014, Bonn,
Geometric quantization and topological recursion
https://www.mpim-bonn.mpg.de/node/5385
29 sept 2014, AIM square meeting, Palo Alto California

Quantum curves, Hitchin systems, and the Eynard-Orantin theory

http://aimath.org/workshops/upcoming/quantumcurves/

Invited talk at ICM, Seoul Korea, august 2014, an overview of the topological recursion, http://www.icm2014.org/
VOD: https://www.youtube.com/watch?v=AZawMZ20Fmk

30 june, 4 jully 2014, Geometry, Quantum Topology and Asymptotics, Genève, http://geneva2014.gatech.edu/.
Video: http://www.youtube.com/watch?v=ZI8e5Xbj4GY
15-20 june 2014, Banff BIRS, Quantum Curves and Quantum Knot Invariants http://www.birs.ca/events/2014/5-day-workshops/14w5073
june 2014, Vienne Austria, Combinatorics, Geometry, and Physics
http://www.mat.univie.ac.at/~kratt/esi3/, canceled.
june 2014 Invited plenary talk at String Math Alberta Canada, summer 2014, https://sites.google.com/a/ualberta.ca/stringmath2014/
26-31 may 2014, Moscou, 4TH WORKSHOP ON COMBINATORICS OF MODULI SPACES, CLUSTER ALGEBRAS, AND TOPOLOGICAL RECURSION
http://www.mccme.ru/lifr/moduli2014/-section=particip.html
28-30 april 2014, Italy, Mirror Symmetry and Spin Curves
Palazzone di Cortona, Italy, April 28 - 30, 2014
Canceled
29 avril 2014, Journées cartes, ENS Paris
march 2014- june 2014, weekly workshops, Groupe de travail, IHES
13-15 february 2014, IHES Physique mathématique des nombres de Hurwitz
12-14 february 2014, JCB Journées combinatoires de Bordeaux
http://www.labri.fr/perso/marckert/JCB-2014.html
30 january 2014, ZMP colloquium DESY Hambourg
18-22 nov 2013, AIM square meeting, Palo Alto California
canceled
2-8 nov 2013, conference IAS, Princeton
canceled
7-oct 2013, Séminaire de Géométrie et Quantification, DMA ENS, at IHP.
3-oct 2013, Jussieu
September 2013, Trieste
http://frompde.sissa.it/workshop2013/
25-30 aout 2013
Banff, http://www.birs.ca/events/2013/5-day-workshops/13w5064/
Cancelled
3-14 juin 2013 Moduli spaces and their invariants in mathematical physics. "Random matrices, Integrability, Moduli spaces and topological recursion"
Montreal, http://www.crm.umontreal.ca/2013/Moduli13/
14 may 2013, 3 hours lecture at ENS Paris: "lecture on the topological recursion".
30-31 may 2013, Conference "Dynamical systems and statistical physics"
91eme "Rencontre entre physiciens théoriciens et mathématiciens",
dynamical systems and statistical physics, Strasbourg.
18-22 march 2013, Quantum Gravity in Paris, Orsay
february 2012, Conference "Topological recursion from matrix models to quantum algebraic geometry".
Aarhus Denmark. QGM
january 2012, School "Topological recursion from matrix models to quantum algebraic geometry".
Aarhus Denmark. QGM
nov 2012, random matrices, from probability to geometry.
Jacques Cartier, Lyon.
24 oct 2012, seminar in Columbia University, Proof of the BKMP conjecture.
oct 2012,
Colloque IPHT, Avignon
sept 2012, Conference "random matrices and random partitions".
Banff, Widom. Canceled
24 sept 2012, "Knot theory and topological recursion".
Saclay.
august 2012, Conference "Topological recursion and BKMP".
square meeting AIM.
18 june 2012, Conference "Mirror symmetry and topological recursion".
Saclay.
2-8 june 2012, Conference "Proof of the BKMP conjecture".
Beijing China.
21-23 may 2012, Integrability.
IHP GranMa conference Its.
15 may 2012, "Pilot process for random curves on random maps".
Séminaire carte Orsay.
16 jan 2012, From random matrices to the geometry of integrable systems,
Seminar Saclay.
december 2011, Lecture series "Topological recursion".
Lecture series, Unige, math department, Geneve.
2010-2011, Combinatorics of random maps.
Lecture series, Unige, math department, Geneve.
october 1st 2011, Group integrals and integrability.
Unige, math department, Geneve.
october 2011, Topological recursion.
New Recursion Formulae and Integrablity for Calabi-Yau Spaces, BIRS Banff.
october 2011, ANR conference: Large Random Matrices.
IHP Paris.
Sept 2011, Enumertive geometry and integrability.
Random Processes, Conformal Field Theory and Integrable Systems, Moscow.
Sept 2011, Lecture series: Maps Enumeration and integrability.
Topical school on Random Processes, Conformal Field Theory and Integrable Systems, St Petersbourg.
august 2011, Lecture series: Maps Enumeration.
Summer School in Random Geometry, Iceland.
july 2011, Matrix models and geometry.
Cargese-Luminy.
june 2011, Matrix models.
Oberwolfach.
april 16, 2011, Spectral curves and integrals over moduli spaces.
CERN, string theory seminar.
april 4, 2011, Statistical models on random lattices.
seminar, Unige, math department, Geneve.
dec , 16 2010, Matrix models and geometry.
Brunel, UK.
dec, 6, 2010, From matrix models to algebraic geometry.
String theory Journal club, CERN, Geneve.
nov , 26 2010, From matrix models to algebraic geometry.
Swiss inter-university meeting on string theory, Ecole Polytechnique Federale, Lausane.
nov, 19 2010, Developpement asymptotique des lois limites de matrices aleatoires et geometrie.
Groupe de travail probas du MAP5, Paris 5.
oct 8, 2010, Matrix models.
Harvard, Boston.
oct 7, 2010, Matrix models.
MIT-Harvard-Northeastern-Brandeis Mathematics Colloquium, Boston.
oct 5, 2010, From matrix models to algebraic geometry.
4 hours lecture, Northeastern, Boston.
sept, 13-17, 2010, Matrix models.
MSRI Berkeley. Canceled
19-23 july 2010, Matrix models and enumerative geometry. Statphys 24, plenary talk, Cairns Australia.
July 2010, On enumerative geometry.
Statphys 24, satellite meeting Brisbane.
july 7th, 2010, On enumerative geometry.
Melbourne, Australia.
May 20, 2010, On enumerative geometry.
Talca, Chile.
May 10-14 2010, On enumerative geometry.
Conference "Symplectic Geometry, Noncommutative Geometry and Physics", MSRI, Berkeley.
May 3-8 2010, On enumerative geometry.
Square meeting AIM, Palo Alto.
april 30 2010, On enumerative geometry.
UC Davis, California.
march 29- april 2, 2010, Liouville theory from matrix models.
StonyBrooks. Canceled
march 29, 2010, Intersection numbers and topological recursion.
Montreal, CRM
march 26, 2010, Hurwitz numbers and topological recursion.
Concordia, Montreal
march 19 2010, Solution of Tutte's equations.
Ottawa
march 16 2010, Symplectic invariants and their applications.
CRM Montreal, theory group seminar.
Winter 2010, Lecture on topological recursion.
Lecture at Saclay. Canceled.
feb 22 2010, Qantum geometrty.
Montpellier
feb 1-5 2010, Matrix models.
UCLA. Canceled
dec 18 2009, A matrix model for plane partitions.
Brunel London. Canceled
dec 3 2009, Quantum algebraic geometry.
LPTHE Jussieu.
dec 2 2009, Large maps and Liouville quantum gravity.
ANR GranMa, IHP.
nov 19 2009, Quantum algebraic geometry.
LPTHE Jussieu.
nov 9-18 2009, Matrix models for topogical strings.
Lisbon, IST, Matrix Models and Geometry CAMGSD Thematic Period @ IST | Fall 2009.
nov 3 2009, Topological recursion relations for Hurwitz numbers.
Lecture at IHP Paris, Statcomb Embedded random graphs (2-6 November 2009).
autumn 2009, Enumeration of maps.
Lecture at IHP Paris.
oct 2009, A matrix model for plane partitions.
STATCOMB, Dimer models and random tilings, oct. 2009.
29/09/2009, Definition of quantum algebraic geometry.
Saclay.
24 july 2009, The topological recursion in matrix models and enumerative geometry, 2.
seminar IHES.
10 july 2009, The topological recursion in matrix models and enumerative geometry.
seminar IHES.
30 june 2009, Random matrices.
ANR GranMa, Lyon.
17-18 june 2009, Random matrices.
IHP Paris.
8-12 june 2009, A matrix model for topological strings.
Recursion structures in topological string theory and enumerative geometry, Palo-Alto, California, USA.
2 june 2009, A matrix model for counting plane partitions.
Conference in honor of Harold Widom, Jussieu.
7 mai 2009, O(n) model.
Orsay Seminaire cartes.
30 avril 2009, Loop equations.
Orsay Seminaire cartes.
8-14/2/2009, Combinatorics of discrete surfaces and random matrices.
Random planar geometry, Les diablerets, Suisse.
2/2/2009, Enumerative Geometry.
Séminaire Grenoble.
20/12/2008, Random matrix methods in enumerative geometry.
The 16th Osaka City University International Academic Symposium 2008 "Riemann Surfaces, Harmonic Maps and Visualization", Osaka.
10-14/12/2008, Symplectic invariants of spectral curves and their applications to enumerative geometry.
Mini Workshop at IPMU A New Recursion from Random Matrices and Topological String Theory, IPMU Tokyo.
14/11/2008, Enumerative Geometry.
Nijmegen, cluster Geometry and quantum theory, bimonthly colloquium.
17/10/2008, Géometrie algébrique et combinatoire.
Batz, colloque de l'IPhT, Canceled.
29/09/2008, Plancherel measure on partitions, matrix models and Gromov-Witten theory.
Université Genève.
12/09/2008, Symplectic invariants of spectral curves and their applications to enumerative geometry.
GIMP conference Geometry and Integrability in Mathematical Physics GIMP'08, Luminy.
08/09/2008, Symplectic invariants of spectral curves and their applications to enumerative geometry.
Misgam Trieste From integrable structures to topological strings and back.
20/06/2008, Universality of matrix models.
Beg Rohu, random matrix school.
2/06/2008, Symplectic invariants of spectral curves and their applications to enumerative geometry.
Marne la vallée, Workshop High-Dimensional Phenomena in Mathematical Physics.
22/05/2008, Symplectic invariants of spectral curves and their applications to enumerative geometry.
Hamburg, seminar Desy theory group.
23/04/2008, Partitions, matrix models and algebraic geometry.
Cambridge, Newton institute, Statistical-Mechanics and Quantum-Field Theory Methods in Combinatorial Enumeration.
14/03/2008, Symplectic invariants of spectral curves.
Munich. Canceled
14/03/2008, Limite des grandes cartes et surfaces de Riemann.
Seminaire cartes a Orsay.
07/03/2008, Solution des equations de Tutte en toute topologie.
Seminaire cartes a Orsay.
14/09/2007, Counting surfaces, from matrix models to algebraic geometry.
Random and integrable models in mathematics and physics, Brussels, 11-15 September 2007.
20/06/2007, Random matrices.
Troisieme rencontre Toeplitz, Probabilites, Matrices Aleatoires, Bordeaux.
12-13/06/2007, Number of maps of any genus, algebraic geometry and integrable hierarchies.
Little workshop on Enumerative topology and random discrete structures, aka "journees cartes et SADA", IHP, Paris, les 12 et 13 juin 2007.
20-21/04/2007, Introduction to matrix models.
Barcelona, Enrage school.
05/04/2007, Matrices aleatoires et combinatoire des cartes.
Orsay.
28/03/2007, Topological expansion and invariants of algebraic curves.
Princeton.
20/03/2007, Topological expansion and invariants of algebraic curves.
CRM Montreal.
14/03/2007, Solution des equations de Tutte.
Lix.
12/03/2007, Topological expansion and invariants of algebraic curves.
LPTHE Jussieu.
30/01/2007, Topological expansion and invariants of algebraic curves.
Saclay.
30/10/2006, Universal random eigenvalues distribution at the birth of a cut transition.
Marseille CIRM programm on Random matrices.
11/07/2006, Geometry and large N expansion of matrix models.
Marseille CIRM programm on Affine Hecke algebra, Langlands programm, conformal field theory and matrix models.
18/05/2006, Large N expansion of matrix models, and algebraic geometry.
Moscow, ANR GIMP conference.
14/03/2006, Large N expansion of random matrix models
Amsterdam.
27/02/2006, Matrices aléatoires, intégrabilité et géométrie algébrique
Orsay.
7/12/2005, Les matrices aléatoires, un outil pour la physique et les mathématiques
Forum de la théorie.
Slides available: .ppt.
15/09/2005, Modèle à 2 matrices, polynômes bi-orthogonaux, problème de Riemann-Hilbert et géométrie algébrique
Soutenance de thèse d'habilitation à diriger les recherches, Paris VII.
Slides available: .pdf.
20/06-8/07/2005, Random matrices, random processes and integrable systems
CRM short program Montréal.
21/05/2005, Large N expansion of Formal matrix models
Zurich, Conference on Random Matrices and Other Random Objects, ETH Zurich, 17-21 mai 2005.
Slides available: .pdf.
3-11/05/2005, Random Matrices, multi-orthogonal Polynomials and Riemann-Hilbert Problems
BIRS Banff.
18/03/2005, Fonctions de corrélations mixtes du modèle à 2 matrices et ansatz de Bethe
Saclay. Abstract:
La valeur moyenne d'une trace de produit de matrices aléatoire, est la fonction génératrice des surfaces discrétisées avec bord. L'ordre des matrices dans le produit décrit les conditions de bords. Par exemple: Tr (M_1^{k} M_2^{l} M_1^{k'} M_2^{l'}) décrit un carré dont le bord contient k conditions 1, suivies de l conditions 2, suivies de k' 1, suivies de l' 2. Les traces mixtes du modèle à 2 matrices décrivent toutes les conditions de bords possible. Elles ne peuvent pas être obtenues comme des dérivées de la fonction de partition. Nous avons pu calculer explicitement toutes les traces mixtes, la solution a la forme d'un ansatz de Bethe.
7/01/2005 - 28/01 /2005 , Cours: Intégrabilité, modèles de matrices et géométrie algébrique.
Saclay.
1. Introduction et généralités sur les matrices aléatoires. Polynômes orthogonaux. Notion de système intégrable et déformations isomonodromiques. Calcul de la courbe spectrale.
2. Méthode des boucles. Développement topologique, interprétation combinatoire. Équation algébrique.
3. Introduction à la géométrie algébrique, exemple des courbes hyper elliptiques.
4. Calculs de différentes observables dans les deux méthodes. Exemples du calcul des asymptotiques de polynômes orthogonaux et calcul du développement de l'énergie libre.
Slides available: affiche.pdf, .ps.
15/10/2004, Surfaces aléatoires discrétisées et diagrammes de Feynmann cubiques sur une surface de Riemann.
Saclay.
Abstract:
le denombrement des surfaces aleatoires est relie au calcul de valeurs moyennes de traces de matrices aleatoires. Plus recement, on a compris que les observables de matrices aleatoires sont reliees a des integrales sur une courbe algebrique. En utilisant les outils puissants de la geometrie algebrique, on se rend compte que toutes les observables de matrices s'obtiennent a partir de diagrammes de Feynmann d'une theorie de champs cubique, dont les propagateurs sont, non-pas les noyeaux de Bergmann, mais les differentielles abeliennes de 3e espece.
05/10/2004, Compter les surfaces aleatoires discretisees de toutes topologies comme des diagrammes de Feynmann sur une surfaces de Riemann.
Saclay.
Abstract:
le denombrement des surfaces aleatoires est un vieux probleme qui a ete relie depuis les annees 80 au calcul de valeurs moyennes de traces de matrices aleatoires. Plus recement, on a compris que les observables de matrices aleatoires sont obtenues comme des integrales sur une surface de Riemann. Je montrerai sur des exemples simples comment ces integrales sur surface de Riemann s'organisent en diagrammes de Feynmann d'une theorie cubique.
Slides available: .pdf, .ps.
23/09/2004, Une loi statistique ``universelle'': la loi des matrices aléatoires.
Saclay, présentation du SPHT pour les nouveaux recrutés du CEA.
Slides available: .ppt
10/06/2004, Asymptotics of orthogonal polynomials.
Les Houches.
Slides available: http://www-spht.cea.fr/articles/t05/036/, http://www-spht.cea.fr/pisp/serban/houches.html.
10/02/2004, Geometry and 1/N expansion of the 2-Matrix model's free energy.
Montréal.
Slides available: .pdf, .ps.
20/01/2004, Présentation des sujets de thèses aux étudiants en DEA.
Saclay.
Slides available: .ppt, .html.
15/05/2003, Topological expansion of the 2-matrix model: the Ising model on a genus one random lattice.
Cracow, Random Geometry k2003 Workshop.
18/03/2003, Une loi statistique ``universelle'': la loi des matrices aléatoires.
Saclay, présentation du SPHT pour les nouveaux recrutés du CEA.
Slides available: .ppt
14/03/2003, Développement à N grand de l'énergie libre du modèle à 2 matrices: modèle d'Ising sur un tore aléatoire.
Saclay.
Abstract:
Dans le développement à N grand de l'énergie libre d'un modèle de matrices, le terme en 1/N^{2h} représente la fonction de partition d'un modèle de physique statistique sur surface aléatoire de genre h. Dans cet exposé, est présentée une méthode pour calculer cette fonction de partition pour tout h, pour le modèle à 2 matrices (Ising). Nous obtenons une expression exacte de la fonction de partition du modèle d'Ising sur un tore aléatoire. La méthode montre un lien très fort avec la géometrie algébrique, et corrobore la conjecture que chaque modèle de matrice est associé à une surface de Riemann et ses proprietés de dualité.
07/03/2003, Modèle à 2 matrices, polynomes bi-orthogonaux, dualité et problème de Riemann-Hilbert.
Saclay.
Abstract:
Le modèle à 2 matrices aléatoires a de nombreuses applications. Entre autres, il permet de représenter les théories conformes minimales (p,q) pour tous p et q, contrairement au modèle à 1 matrice qui ne permet de représenter que q=2. Nous avons mis en évidence que les polynomes bi-orthogonaux associés à ce modèle, satisfont des systèmes différentiels possédant une élégante proprieté de dualité. Nous avons également pu formuler le problème de Riemann-Hilbert qui leur correspond. Ceci devrait par la suite permettre d'étudier les proprietés universelles de la statistique spectrale (et toutes les applications physiques qui en découlent), et faire le lien encore mysterieux avec les systèmes intégrables.
07/01/2003, Modèle à 2 matrices, polynomes bi-orthogonaux, dualité et problème de Riemann-Hilbert.
Jussieu.
09/12/2002, Points critiques des modèles de matrices et la hiérarchie de Painlevé II.
Saclay, SPHT.
08/10/2002, Points critiques des modèles de matrices et la hiérarchie de Painlevé II.
CRM, Montréal. Mathematical Physics's weekly seminar.
Abstract:
Au point critique, la densité de valeurs propres s'annule avec un degré 2m. Nous calculons les comportements asymptotiques des polynomes orthogonaux associés (qui permettent de calculer toutes les fonctions de corrélations de valeurs propres) dans cette limite, en fonction de m. Ceci n'etait connu que pour m=1, dans le cas pair (spectre symmetrique). Nous trouvons que les asymptotiques sont solution d'un système d'équations différentielles associé à la hiérarchie de Painlevé II.
04/05/2002, Genus zero large n asymptotics of bi-orthogonal polynomials involved in the random 2-matrix model.
AMS Meeting, Montréal, Special Session on Asymptotics for Random Matrix Models and Their Applications.
Abstract:
The biorthogonal polynomials related to the random 2-matrix model, obey two dual systems of differential equations. We have derived the Riemann Hilbert problem corresponding to them, and this opens the route to nd the large n asymptotics. As a simpli cation, we consider here only the case where the spectral curve of the di erential system has genus zero (also called 1-cut case). We present here the genus zero large n asymptotics for the biorthogonal polynomials, derived by the random-matrix "saddle point method". These asymptotics should then be used as the starting point for unfolding the Riemann Hilbert methods which were very succesfull for the ordinary orthogonal polynomials.
30/08/2001 , An alternative method for finding large N asymptotics of (skew-)orthogonal polynomials (β= 1,2,4).
CRM, Montréal, Workshop on spectral statistics and high-energy eigenstates.
20/06/2001 , Duality in differential equations, bi-orthogonal polynomials, and random matrices.
Poster at the rencontres Itzykson Saclay.
Abstract:
- finding pairs of dual differential systems.
- study the differential equations satisfied by bi-orthogonal polynomials.
- study the statistical distribution of eigenvalues of two coupled random matrices.
05/03/2001 , Polynomes anti-orthogonaux et matrices aléatoires-Une méthode pour obtenir les asymptotiques.
Paris V.
Abstract:Many physical systems can be represented by a random matrix, and they share some universal properties. The method of Orthogonal Polynomials was invented in order to understand universality in random matrices (skew-orthogonal polynomials for non hermitian matrices). I will briefly introduce the subject, and show how one can derive some asymptotics for the skew-orthogonal polynomials.
13/02/2001 , The Random-Matrix O(n) Model.
CRM, Montreal. Mathematical Physics's weekly seminar.
Abstract:The O(n) model is a famous toy model for 2D statistical physics. When put on a random lattice, the O(n) model is coupled to gravity, and the partition function can be represented by a matrix integral. The large n limit of that integral can be computed, the results involves elliptical functions even in the one cut-case (because there is another "ghost" cut). The O(n) model is very rich because it interpolates all the possible (p,q) conformal minimal models, as well as non-rational cases.
30/01/2001 , Random matrices and (skew)-orthogonal polynomials.
CRM, Montreal. Mathematical Physics's weekly seminar.
Abstract:Many physical systems can be represented by a random matrix, and they share some universal properties. The method of Orthogonal Polynomials was invented in order to understand universality in random matrices (skew-orthogonal polynomials for non hermitian matrices). I will briefly introduce the subject, and show how one can derive some asymptotics for the skew-orthogonal polynomials.
16/11/2000 , Quantum Field Theory and Mathematical Physics.
Saclay's quantum field theory and mathematical physics 1998-2000 activity report.
Slides available: .pdf, .ps.
22/09/2000 - 24/11 /2000 , Cours: les Matrices Aléatoires.
Saclay.
1. Introduction: Les matrices aléatoires en Physique.
2. Les ensembles de matrices aléatoires.
3. Développement diagrammatique.
4. La méthode du col.
5. La méthode des Polynômes orthogonaux.
6. La méthode des équations du mouvement.
7. La double limite d'échelle, hiérarchies intégrables.
Slides available: affiche.ps, .ps.
28/09/2000 , On random matrix models with disconnected eigenvalues support.
København, NBI, Eurogrid seminar.
Abstract: When the support of eigenvalues is not connected, the famous 1/N^2 topological expansion of the free energy of matrix models breaks down. Some small corrections to the free energy can then turn dominant for the correlation functions, leading to additional terms which were forgotten in the litterature so far. The origin of those corrections lies in the discreteness of the spectrum, and has nothing to do with any symmetry of the potential as it was sometimes assumed.
Slides available: .pdf, .ps.
08/06/2000 , The Potts-Model on a random lattice, some exact results.
Montreal, CRM.
Abstract: The Potts Model on a random lattice can be represented by use of a random matrix model. We have found the equations of motion of this model, which happen to be solvable due to their similarity with the O(n) model (apparently n=q-2). We thus find some explicit exact solution of the Potts model. The difference between Potts-q and O(n=q-2) lies in the different boundary conditions. The Potts model is then comparable to the O(n) model with q=n^2.
21/03/2000 , Problèmes de coloriages.
Paris 7.
Slides available: .pdf, .ps.
25/02/2000 , Modèles de matrices dans le cas d'une distribution à support non connexe.
Saclay.
Abstract: Il y a 2 ans, Brezin et Deo découvraient une étonnante contradiction entre la fonction de corrélation des valeurs propres d'une matrice aléatoire, calculée par la méthode des équations du mouvement ou calculée par la méthode des polynomes orthogonaux. Lorsque le support des valeurs propres n'est pas connexe, il n'y a pas de développement topologique. Nous avons résolu ce paradoxe et calculé dans le cas général la fonction de corrélation. (Travail effectue avec G. Bonnet et F. David)
Slides available: .pdf, .ps.
25/01/2000 , Les matrices aléatoires en physique: de la physique des solides à la théorie des cordes.
Paris 7
Abstract: Les champs d'applications des modeles de matrices aleatoires couvrent presque tous les domaines de la physique. En effet, tout systeme ou sont couples un grand nombre de degres de libertes est naturellement represente par une matrice (matrice de transfert ou de diffusion dans les conducteurs, hamiltonien en mecanique quantique, champs de jauges non commutatifs en theories quantique des champs, etc...). Et des que le systeme que l'on veut modeliser contient du desordre (impuretes dans les conducteurs) du chaos (trop complexe pour faire des calculs exacts) ou un caractere aleatoire fondamental (mecanique quantique), les matrices aleatoires fournissent un cadre de travail adapte et des outils mathematiques efficaces. Nous passerons rapidement en revue les principales applications des matrices aleatoires hermitiennes:
1. La limite gaussienne: conducteurs mesoscopiques, chaos quantique.
2. Les points critiques: surfaces aleatoires, physique statistique et theories conformes, theorie des cordes, gravitation quantique.
3. Les modeles supersymetriques: M-theory.
22/05/98 , Tri-coloured graphs and matrices.
Heriot-Watt Univeristy, department of mathematics, Edimburgh.
Abstract:
in how many ways can one colour the edges of a 3-coordinate lattice with 3 colours, so that two following links are of different colours ? This is the generalization of the Baxter 3-colour problem to a random lattice. A matrix model formulation, gives a set of equations, which answer partially the question at least perturbatively, and we find the critical points. A generalization of this matrix model allows to enumerate the hamiltonian paths on a random lattice.
07/05/98 , 5 minutes presentation, Durham.
Durham.
02/12/97 , 2 models for enumerating tri-couloured graphs.
NBI, København.
Slides available: .html.
07/10/97 , Random Matrices.
Durham.
18/09/97 , Présentation de 5 minutes.
Saclay.
15/09/97 , Correlations de valeurs propres dans la limite N->\infty.
Saclay.