Du 12 au 14 juin 2014
IRMA
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 content of this conference has been published by Springer here and is also avalaible on ArXiv.
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
-
Jeudi 12 juin 2014
-
09:30
Norbert A'campo, Basel
From Riemann to quantics
-
10:30
Pause -
11:00
Charles Frances, Orsay
Lorentz manifolds with noncompact isometry group
Abstract.--- 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. -
14:30
Nicolas Bergeron, Orsay
Theta series and special algebraic cycles in ball quotients
-
15:30
Pause -
16:00
Renzo Ricca, Milan
From “multiple continuity” to modern topological field theory
Abstract.--- 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 multi-valuedness 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) re-considered and adapted Green’s theorem for a multiply-connected domain [2]. In this talk we review these original contributions, by showing how these concepts had an immediate impact in contemporary science and a long-term relevance in modern research, from the discovery of the Aharonov-Bohm 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, 105-110. [2] Thomson, W. (Lord Kelvin) (1869) On vortex motion. Trans. Roy. Soc. Edinburgh 25, 217-260. [3] Ricca, R.L. (2009) Structural complexity and dynamical systems. In Lectures on Topological Fluid Mechanics (ed. R.L. Ricca), pp. 169-188. Springer-CIME Lecture Notes in Mathematics 1973 (Springer-Verlag, Heidelberg). -
19:30
Dîner Offert Tous Les Participants Restaurant "le Petit Bois Vert"
Adresse : 2 quai de la Bruche (Quartier petite France)
-
Vendredi 13 juin 2014
-
09:30
Joël Merker, Orsay
Rational aspects of holomorphic vector bundles on projective algebraic varieties and of Cartan connections in CR geometry
Abstract.--- This talk will present partly achieved and partly programmatic effective features of the computations of Cartan curvatures in Cauchy-Riemann 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. -
10:30
Pause -
11:00
Catherine Meusburger, Erlangen
Generalised shear coordinates on moduli spaces of (2+1)-spacetimes
Abstract.---The diffeomorphism invariant phase spaces of (2+1)-gravity are
moduli spaces of maximal globally hyperbolic constant curvature
(2+1)-spacetimes with the curvature given by the cosmological constant.
We consider spacetimes with cusped Cauchy surfaces S and parametrise
these moduli spaces in terms of shear coordinates and measured geodesic
laminations on S. This leads to a very simple description of their
symplectic structure in terms of the cotangent bundle of Teichmueller
space and can be viewed as analytic continuation of shear coordinates.
We derive the action of the mapping class group Mod(S) on these moduli
spaces and show that it preserves the symplectic structure. This leads
to three different mapping class group actions on the cotangent bundle
of Teichmueller space, which involve the cosmological constant as a
parameter and are generated by a Hamiltonian. We discuss the
interpretation of these results in (2+1)-gravity and their implications
for quantisation.
This is joint work with Carlos Scarinci, arXiv:14022575 -
14:00
Dmitry Zvonkine, Jussieu
Cohomological relations on Mbar_{g,n} via 3-spin structures
Abstract.--- 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 3-spin Witten class and the Givental-Teleman classification of semi-simple 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 r-spin 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. -
15:00
Pause -
15:30
Alexey Sossinsky, Moscou
Artin's spherical braid group, Dirac's electron spin, and the Riemann surface of 4th degree elliptic curves
Abstract.--- 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(z-1)(z-2)(z-3)]^{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. -
16:30
Lizhen Ji, Ann Arbor
Riemann's moduli space: a historical perspective
Abstract.--- 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 well-known but important results of Teichmuller, Weil and Grothendicek. This talk is based on joint work with Noerbert A'Campo and Athanase Papadopoulos -
18:00
Réception La Mairie (place Broglie) Tous Les Participants Sont Invités
On partira tous ensemble de l'IRMA à 17h30 après la conférence
-
Samedi 14 juin 2014
-
09:00
François David, CEA
Planar maps, circle patterns, conformal point processes and 2D gravity
Abstract.--- 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). -
10:00
Pause -
10:30
Frédéric Lassiaille, Toulon
Gravitational model of the three elements theory : mathematical details
Abstract.--- 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 space-time 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.