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Accueil du site > Agenda > Colloques et rencontres > Archives > Agenda 2011 > 88e rencontre entre physiciens théoriciens et mathématiciens : Discrétisation en mathématiques et en physique
IRMA, 810 september 2011
La 88ème rencontre entre physiciens théoriciens et mathématiciens aura pour thème la discrétisation en mathématiques et en physique.
The 88th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on September 810, 2011. The theme will be : "Discretization in Mathematics and in Physics".
Organizers : Dmitry Millionschikov and Athanase Papadopoulos
The invited speakers include :
Ivan Dynnikov (Moscou)
Vladimir Fock (Strasbourg)
Piotr Grinevich (Moscou)
Rinat Kashaev (Genève)
Satya Majumdar (LPTMS, Orsay)
Sergei Nechaev (LPTMS, Orsay)
Valentin Ovsienko (Lyon)
Yuri Suris (TU Berlin)
Alexander Veselov (Loughborough)
JeanBernard Zuber (Paris 6)
Talks are in English. Some of the talks will be survey talks intended for a general audience.
Graduate students and young mathematicians are welcome. Registration is required (and free of charge), at the following link Hotel booking can be asked for through the registration link.
For questions please contact the organizers :
Dmitry Millionschikov
Athanase Papadopoulos


09h00 
Rinat Kashaev  Université de GenèveQuantum Teichmüller theory and TQFTAbstract : Quantum Teichmüller theory leads to specific unitary projective representations of mapping class groups of punctured surfaces, where, among other things, some integrable discrete equations can be realized as mapping class dynamics. These representations arise as representations of bigger algebraic structures called Ptolemy groupoids which can also be thought as parts of certain combinatorial cobordism categories. In this way it is natural to expect that quantum Teichmuller theory is a part of TQFT. I will show that such TQFT does indeed exist. The talk is partially based on a joint work with Joergen Ellegaard Andersen. 


10h00 
Alexander Veselov  Loughborough UniversityYangBaxter maps and discrete integrabilityThis talk will be addressed to a nonspecialized audience. 


11h00 
Coffee break 


11h30 
Satya Majumdar  Université de ParisSud, Laboratoire de physique théorique et modèles statistiquesRandom Convex Hulls and Extreme Value StatisticsAbstract : Convex hull of a set of points in two dimension roughly 


14h00 
Piotr Grinevich  Université de Moscou et Institut LandauAn integrable at one energy elliptic discretization for the 2dimensional Schrodinger operatorWe show that a special elliptic (5point) discretization of the 2dimensional Schrodinger operator in integrable at one energy level. Abstract : Integrability means, that this problem admits a wide class of exact (thetafunctional) solutions and infinitedimensional algebra of symmetries, generates by an analog of Toda hierarchy with 2 discrete spatial variables. This hierarchy can be also treated as discretization of the NovikovVeselov hierarchy. 


15h00 
coffee break 


15h30 
Alexei Penskoi  Univérsité de Moscou, laboratoire BogolyubovLaplace transformations and spectral theory of twodimensional semidiscrete hyperbolic Schroedinger operatorsAnbtract : In this talk we introduce Laplace transformations of 2D 


17h00 
Boat trip around the old city of Strasbourg (the boat trip is offered to the participants by the Mayor of Strasbourg) 


19h00 
Dinner offered to the participants at the restaurant "petit Bois Vert". The address is: 2 quai de la Bruche (Petite France region in the historica center of Strasbourg) 


10h00 
Serguei Nechaev  Université de ParisSudOn shock’s statistics in "Tetris" gameAbstract :
We consider a (1 + 1) dimensional ballistic deposition process with
nextnearest neighbor interactionwhich belongs to the
KardarParisiZhang universality classand introduce for this
discrete model a
variational formulation similar to that for the randomly forced
continuous Burgers equationThis allows to identify the 


11h00 
Coffe break 


11h30 
Yuri Suris  Technische Universität BerlinOn the Lagrangian structure of integrable quadequationsAbstract : The new idea of flip invariance of action functionals in multidimensional lattices was recently highlighted as a key feature of discrete integrable systems. After having been demonstrated for several particular cases of integrable quadequations by BazhanovMangazeev Sergeev and by LobbNijhoff, the flip invariance was given a simple and caseindependent proof for all integrable quadequations in my joint work with Bobenko. This result was also extended to asymmetric quadequations in my joint work with Boll. Moreover, a new relation for Lagrangians within one elementary quadrilateral was found which seems to be a fundamental building block of the various versions of flip invariance. The talk will be devoted to these results and will provide necessary background informations, as well. 


14h00 
Vladimir Fock  StrasbourgDimers and integrable systemsAbstract : A.B.Goncharov and R.Kenyon discovered a family of integrable systems enumerated by convex polygons on a plane with vertices in integral pointsThe collection of integrals is given by a partition function of a dimer models on a 2D torus and the phase space has a natural cluster structureWe will explain their construction as well as some examplesfitting into this scheme and taking place on symplectic leaves of loop groupsIn particular we will reinterpret in this way relativistic Toda chainSchwarzOvsienkoTabachnikov discrete integrable system on the space of polygons and certain discretisations of the mKdV equations 


15h00 
Coffe break 


15h30 
Olga Kravchenko  Université Claude Bernard, LyonAlgebraic operadic structures on links and knotsAbstract : Algebraic structures, such as Lie, associative or commutative, make their appearances in many areas of mathematics. Recently it turned out that there are a few beautiful variations of these classical algebraic structures. Starting from defining a Leibniz algebra (similar to Lie but without the antisymmetry condition) J.L. Loday and his collaborators have discovered several other structures. The right framework for their description comes from algebraic topology and is called Theory of operads. In the talk I will give a brief introduction to operads and algebraic structures. Then I will show some examples of algebraic structures found in the theory of knot and tangle invariants based on my joint work with M. Polyak. 


16h30 
Valentin Ovsienko  Université Claude Bernard, LyonThe pentagram map and generalized friezes of Coxeter This talk will be addressed to a nonspecialized audience. 


18h00 
Reception at the city hall (mairie)offered by the Mayor of Strasbourg. 


09h00 
Ivan Dynnikov  Université de Moscou et Institut SteklovA discretization of complex analysisThis talk will be accessible to a nonspecialized audience. 


10h00 
Coffe break 


10h30 
Sergey V. Smirnov  Université de MoscouIntegrable semidiscrete Toda latticesAbstract : Integrable boundary conditions for twodimensional Toda lattice are known to be described by Cartan matrices of semisimple Lie algebras since the beginning of 1980es. Various approaches have been used in the continuous case by Mikhailov, Shabat and Yamilov, Adler, Habibullin and Gurel and by many others. Onedimensional discrete Toda chains have been studied by Suris in 1990. The situation in (semi)discrete case is much more complicate. In both cases no analogs of B and D series are yet known. In purely discrete case the C series was examined by Habibullin in 2006. My talk will be focused on the semidiscrete caseI'll expalain how Lax presentation for the Cseries lattice can be obtained using two Lax pairs for the infinite lattice and I'll show how the symmetry approach can be used to classify integrable boundary conditions of a certain type for the semidiscrete Toda lattice. 
Dernière mise à jour le 22072011