Du 20 au 22 septembre 2012
IRMA
La 90ème rencontre entre physiciens théoriciens et mathématiciens aura pour thème : Lie et Klein ; le programme d'Erlangen et son impact en physique et en mathématique.
The 90th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on Septembre 20-22, 2012. The theme will be : "Lie and Klein; the Erlangen program and its impact on mathematics and physics".
Organizers: Lizhen Ji and Athanase Papadopoulos
Invited Talks :
- Norbert A'Campo (Bâle)
- Gérard Besson (Grenoble)
- Jean-Michel Bismut (Orsay)
- Pierre Cartier (IHES)
- Hubert Goenner (Göttingen)
- Misha Gromov (IHES) ; to be confirmed.
- Frances Kirwan (Oxford) ; to be confirmed.
- Vladimir Matveev (Jena)
- Catherine Meusburger (Erlangen)
- Pierre Py (Strasbourg)
- Jean-Marc Schlenker (Toulouse)
- Alexei Sossinsky (Moscou)
- Yuri Suris (Berlin)
- Alexander Vinogradov (Salerno)
- Anna Wienhard (Princeton)
- Jean-Bernard Zuber (Paris 6)
The content of this conference has been published by EMS here.
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 practical and other questions please contact the organizers :
- Lizhen Ji : lji@umich.edu
- Athanase Papadopoulos : athanase.papadopoulos@math.unistra.fr
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Jeudi 20 septembre 2012
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09:00
Pierre Cartier, IHES
Infinite Lie groups
ABSTRACT : In this lecture , I plan to make a historical review of the infinite-dimensional Lie groups , more properly called now "pseudo-groups" after Ehresmann . We shall see how categories and groupoids were the natural outcome of these developments, and how this remained a very active field of research , long after Ehresmann's death . I shall show how Erlangen program was one of the driving forces behind Bourbaki's entreprise . I shall finish by showing how Gauge Fields in physics are the legitimate brainchildren of these mathematical methods . -
10:00
Pause/coffee Break
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10:30
Norbert A'campo, Basel
Natural symetries of manifolds after Whittaker, Filipkiewicz and Takens
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11:30
Catherine Meusburger, Erlangen
Dirac gauge fixing and dynamical classical r-matrix symmetries in (2+1)-gravity
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14:00
Anna Wienhard, Heidelberg
Anosov representations, domains of discontinuity and geometric structures
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15:00
Pause/coffe Break
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15:30
Yuri Suris, Berlin
Erlangen Program and Discrete Differential Geometry
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16:30
Departure From Irma For A Boat Trip Offered To All Paricipants
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18:30
Dinner Offered To All Participants Restaurant Le Petit Bois Vert (petite France Quarter)
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Vendredi 21 septembre 2012
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09:00
Jean-Michel Bismut, Orsay
Hypoelliptic Laplacian and the trace formula
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10:00
Pause/coffee Break
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10:30
Alexandre Vinogradov, Salerno
Assembling Lie algebras from lieons
ABSTRACT : If a Lie algebra structure g on a vector space is the sum of a family of mutually compatible Lie algebra structures g_i we say that g is simply assembled from g_i's. By repeating this procedure several times one gets a family of Lie algebras assembled from g_i's. The main result is that any finite dimensional Lie algebra over the reals or over an algebraically closed field can be assembled from two constituents, called d- and p-lieons. A lieon is the direct sum of an abelian Lie algebra and either the 2-dimensional nonabelian Lie algebra or the 3-dimensional Heisenberg algebra. Various results concerning assembling-disassembling procedures with Lie algebras will be shown. In particular, all "molecules" (coaxial Lie algebras), which can be simply assembled from lieons, will be described. I plan also to discuss numerous problems and perspectives concerning this "Lie chemistry". -
11:30
Pierre Py, Strasbourg
SO(n,1) and exotic CAT(0) spaces
ABSTRACT : In the spirit of Klein's Erlangen program, we will discuss the following question. Let Isom (H^n) be the isometry group of the real hyperbolic space H^n of dimension n. Besides the hyperbolic space itself, on which nonpositively curved spaces can the group Isom(H^n) act? -
14:30
Vladimir Matveev, Jena
Lie modification of the Klein Erlangen program for Riemannian geometry and the solution of two problems of Sophus Lie
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15:30
Pause/coffee Break
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16:00
Jean-Marc Schlenker, Toulouse
3-dimensional Anti-de Sitter geometry and its applications
ABSTRACT : The 3-dimensional anti-de Sitter space is a Lorentzian space of constant curvature -1, which can be considered as a Lorentzian analog of the hyperbolic space. It was originally introduced as a model for cosmology, but it also has some deep relations to Teichmüller theory. We will outline some geometric properties of the AdS_3 and indicate how they are related to statements on hyperbolic surfaces. -
17:00
Hubert Goenner, Goettingen
Weak Lie symmetry
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18:30
Reception By The Mayor At The Town Hall (departure From Irma At 18h10)
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Samedi 22 septembre 2012
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09:00
Jean-Bernard Zuber, Paris
Invariances in Physics and Group Theory
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10:00
Pause/coffee Break
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10:30
Alexey Sossinski, Moscow
The heritage of Sophus Lie and Felix Klein in the teaching of mathematics
ABSTRACT : It is remarkable that the revolutionary ideas of Klein and Lie in geometry and differential equations have had so little influence in the teaching of mathematics at the university level up to the present time. In the talk, following Klein, I will explain that there is no such {\it science} as "geometry", but there are mathematical {\it objects} that may be called "geometries" (namely sets with a transformation group acting on the set) which should be studied from that point of view. These objects are the objects of a category (morphisms being equivariant maps), and the category language (not necessitating any category theory) is the appropriate one for their study. Further, I will try to show that the ideas of Lie concerning the symmetry of differential equations are not only a powerful tool in solving ODE as well as PDE, but conceptually make it much easier for students to understand what a differential equation actually is and should appear in introductory differential equation courses at university level not only for future mathematicians but especially for future physicists and engineers. If time permits, I will indicate what books can be used for teaching mathematics in this way or may be modified to become standard textbooks.