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Accueil du site > Agenda > Colloques et rencontres > Archives > Agenda 2014 > 93e rencontre entre mathématiciens et physiciens théoriciens : Riemann, la topologie et la physique
IRMA, 1214 juin 2014
La 93ème rencontre entre mathématiciens et physiciens théoriciens aura pour thème : Riemann, la topologie et la physique.
The 93th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on June 12, 13, 14 2014. The theme will be : "Riemann, topology and physics".
Organizers : Lizhen Ji (Michigan) and Athanase Papadopoulos (Strasbourg)
The invited speakers include :
Norbert A’Campo (Basel)
Nicolas Bergeron (Jussieu)
François David (CEA)
Charles Frances (Orsay)
Jeremy Gray (Open Univ. UK)
Joël Merker (Orsay)
Catherine Meusburger (Erlangen)
Sergey Natanzon (Moscou)
Bob Penner (Caltech et Aarhus)
Renzo Ricca (Milano)
Alexey Sossinsky (Moscou)
Dmitri Zvonkine (Jussieu)
The talks will be 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 this link. Hotel booking can be asked for through the registration link.
For practical and other questions please the organizers :
Lizhen Ji : lji@umich.edu
Athanase Papadopoulos : athanase.papadopoulos@math.unistra.fr


09h30 
Norbert A’campo  BaselFrom Riemann to quantics 


10h30 
Pause 


11h00 
Charles Frances  OrsayLorentz manifolds with noncompact isometry groupAbstract. A celebrated result of Myers and Steenrod says that the isometry group of a compact Riemannian manifold is a compact Lie group. This compactness property is no longer true for Lorentz structures. In this talk, we will review some results about the topology of compact Lorentz manifolds admitting a noncompact isometry group, and we will present new developments in dimension 3. 


14h30 
Nicolas Bergeron  OrsayTheta series and special algebraic cycles in ball quotients



15h30 
Pause 


16h00 
Renzo Ricca  MilanFrom “multiple continuity” to modern topological field theoryAbstract. One of Riemann’s great contributions to modern aspects of topological field theory is rooted in his paper of 1857 [1], where he introduced the concept of “multiple continuity” of an ambient domain and the effect of this on the multivaluedness of a potential defined in this domain. Riemann’s considerations were immediately noted by Helmholtz, who soonafter (1858) derived his conservation laws of vortex motion, thus establishing the foundations of topological fluid mechanics. Motivated by his vortex atom theory, William Thomson (later Lord Kelvin) reconsidered and adapted Green’s theorem for a multiplyconnected domain [2]. In this talk we review these original contributions, by showing how these concepts had an immediate impact in contemporary science and a longterm relevance in modern research, from the discovery of the AharonovBohm effect in quantum theory to the most recent developments in topological aspects of dynamical systems and classical field theory, such as vortex dynamics and magnetohydrodynamics. [1] Riemann, G.F.B. (1857) Lehrsätze aus der analysis situs für die Theorie der Integrale von zweigliedringen vollständingen Differentialien. J. Marhematik 54, 105110. [2] Thomson, W. (Lord Kelvin) (1869) On vortex motion. Trans. Roy. Soc. Edinburgh 25, 217260. [3] Ricca, R.L. (2009) Structural complexity and dynamical systems. In Lectures on Topological Fluid Mechanics (ed. R.L. Ricca), pp. 169188. SpringerCIME Lecture Notes in Mathematics 1973 (SpringerVerlag, Heidelberg). 


19h30 
Dîner Offert Tous Les Participants Restaurant "le Petit Bois Vert"Adresse : 2 quai de la Bruche (Quartier petite France) 


09h30 
Joël Merker  OrsayRational aspects of holomorphic vector bundles on projective algebraic varieties and of Cartan connections in CR geometryAbstract. This talk will present partly achieved and partly programmatic effective features of the computations of Cartan curvatures in CauchyRiemann geometry and of coordinate constructions of holomorphic sections of jet bundles on the route towards Kobayashi's hyperbolicity conjecture, accompanied with a few historical hints on Riemann's Open Philosophy of Mathematics. 


10h30 
Pause 


11h00 
Catherine Meusburger  ErlangenGeneralised shear coordinates on moduli spaces of (2+1)spacetimesAbstract.The diffeomorphism invariant phase spaces of (2+1)gravity are 


14h00 
Dmitry Zvonkine  JussieuCohomological relations on Mbar_{g,n} via 3spin structuresAbstract. We construct a family of relations between tautological cohomology classes on the moduli space Mbar_{g,n}. This family contains all relations known to this day and is expected to be complete and optimal. The construction uses the Frobenius manifold of the A_2 singularity, the 3spin Witten class and the GiventalTeleman classification of semisimple cohomological field theories (CohFTs) I will start with a short introduction into the cohomology of moduli spaces and give simplest examples of tautological relations. Then I will proceed to define Witten's rspin class, explain why it is a CohFT and how Teleman's classification applies to it. If time permits I will compute a couple of cohomological relations using our method. This is a joint work with R. Pandharipande and A. Pixton. 


15h00 
Pause 


15h30 
Alexey Sossinsky  MoscouArtin’s spherical braid group, Dirac’s electron spin, and the Riemann surface of 4th degree elliptic curvesAbstract. This talk is about ancient history: the physics goes back to the 1920ies, the mathematics to the 1960ies (and to Riemann's work of the19th century). My motivation for recalling this remarkable instance of interaction between mathematicians and physicists is that I have found that most of the physicists I know are not really familiar with the underlying mathematics, while my mathematician friends are not aware of the beautiful physics that the math involves. Another reason is that there are some question in my mind that remain unanswered, and perhaps some of the participants will help me answer them. The spherical braid group SB(n) is obtained from Artin's classical braid group B(n) by adding one extra relation to those defining B(n). The key mathematical points of the talk is that the group BS(n), unlike B(n), has finite order elements, that the fundamental group of SO(3) is Z/2Z, and that the Riemann surface for elliptic curve given by w= [z(z1)(z2)(z3)]^{1/2} is the torus. The story from the physical viewpoint involves Dirac's theory of electron spin and his famous experiment ("Dirac's string trick"). I will try to elucidate the relationship between all these notions and facts. In the process, some beautiful computer graphics and animations will be demonstrated. 


16h30 
Lizhen Ji  Ann ArborRiemann’s moduli space : a historical perspectiveAbstract. In his short life, Riemann made many deep important contributions to multiple subjects in mathematics. For example, he introduced the notion of Riemann surfaces and raised the problem on moduli space of Riemann surfaces. Both have far reaching consequences in analysis, algebraic geometry, topology etc. In this talk, I will give an overview of the history of the moduli space of Riemann surfaces and the closely related Teichmuller space, emphasizing some not so wellknown but important results of Teichmuller, Weil and Grothendicek. This talk is based on joint work with Noerbert A'Campo and Athanase Papadopoulos 


18h00 
Réception La Mairie (place Broglie) Tous Les Participants Sont InvitésOn partira tous ensemble de l’IRMA à 17h30 après la conférence 


09h00 
François David  CEAPlanar maps, circle patterns, conformal point processes and 2D gravityAbstract. A model of random planar triangulations is presented. It exemplifies the relations between discrete geometries in the plane (circle packings and circle patterns), conformally invariant point processes and two dimensional quantum gravity (topological gravity and Liouville theory). 


10h00 
Pause 


10h30 
Frédéric Lassiaille  ToulonGravitational model of the three elements theory : mathematical detailsAbstract. The aim is to parse the mathematical details related to the gravitational model of the three elements theory [1]. This model is proven to be coherent and really compatible with relativity. The Riemannian representation of spacetime which is used in this model is proven to be legal. It allows to understand relativity in a more human sensitive manner than Minkowskian usual representation. 
Dernière mise à jour le 2042014