Du 8 au 10 juin 2017
IRMA
La 99ème rencontre entre mathématiciens et physiciens théoriciens aura pour thème : Géométrie et physique. Elle est dédiée à la mémoire de W. P. Thurston.
The 99th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on June 8-10, 2017. The theme will be : Geometry and physics. It is dedicated to the memory of W. P. Thurston.
Organizers : Vincent Alberge (New York), Ken'ichi Ohshika (Osaka) and Athanase Papadopoulos (Strasbourg)
The invited speakers include :
- Norbert A'Campo (Basel)
- Daniele Alessandrini (Heidelberg)
- Valeriy Berestovskiy (Novosibirsk)
- Francesco Bonsante (Pavia)
- George Daskalopoulos (Brown)
- François Fillastre (Cergy)
- Louis Funar (Grenoble)
- Hubert Goenner (Goettingen)
- Shinobu Hosono (Tokyo)
- Rinat Kashaev (Genève)
- Gaël Meigniez (Vannes)
- Hideki Miyachi (Osaka)
- Dylan Thurston (Bloomington)
- Richard Wentworth (Maryland)
- Sumio Yamada (Tokyo)
- Mahmoud Zeinalian (New York)
Venue: Salle de conférences, IRMA building
The talks will be in English. Some of them will be survey talks intended for a general audience.
Graduate students and young mathematicians are welcome.
Registration is free of charge but the potential participants are asked to contact one of the organisers:
- Vincent Alberge : valberge AT fordham.edu
- Ken'ichi Ohshika : ohshika AT math.sci.osaka-u.ac.jp
- Athanase Papadopoulos : athanase.papadopoulos AT math.unistra.fr
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Jeudi 8 juin 2017
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09:00
Norbert A'campo, Basel
Uniformisation Theorem of genus > 1 Riemann Surfaces
Abstract: The Gauss-Bonnet equality and inequality and Thurton's lesson: " Use geometry, especially hyperbolic geometry," provide a more elementary proof. -
10:00
Coffee Break
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10:30
Louis Funar, Grenoble
Cantor surfaces and mapping class groups
Abstract: Smooth mapping class groups of compact surfaces punctured along Cantor sets have strong finiteness properties and they are closely related to Thompson groups. Similar constructions in higher dimensions can be used to recover Brin's finitely presented groups. -
11:30
François Fillastre, Cergy
On the space of flat metrics with conical singularities on a compact surface
Abstract : By a result of W.~P. Thurston, the moduli space of flat metrics on the sphere with prescribed n cone singularities of positive curvature is a complex hyperbolic orbifold of dimension n-3. The Hermitian form comes from the area of the metric. Using geometry of Euclidean polyhedra, we observe that this space has a natural decomposition into real hyperbolic convex polyhedra of dimensions n-3 and \leq 1/2(n-1). By a result of W.~Veech, the moduli space of flat metrics on a compact surface with prescribed cone singularities of negative curvature has a foliation whose leaves have a local structure of complex pseudo-spheres, coming again from the area of the metric. The form can be degenerate; its signature depends on the collection of angles. Using polyhedral surfaces in Minkowski space, we show that this moduli space has a natural decomposition into spherical convex polyhedra. -
14:00
Shinobu Hosono, Tokyo
Mirror symmetry and birational geometry of CICYs
Abstract: After making a quick survey of the "classical" mirror symmetry in 90's, I will discuss two interesting examples of complete intersection Calabi-Yau manifolds (CICYs) which have birational automorphisms of infinite order. I will describe the mirror symmetry (mirror family) of these Calabi-Yau manifolds, and observe that the birational automorphisms correspond nicely to certain monodromy transformations of the family. If time permit, I will show "Picard-Lefschetz monodromy" which corresponds to flopping curves. This talk is based on collaborations with Hiromichi Takagi. -
15:00
Coffee Break
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15:30
Hideki Miyachi, Osaka
Towards complex analysis on Teichmüller space with Thurston's theory
Abstract: Teichmüller space is studied and applied from several points of view. In this talk, I will give my recent progress on an attempt to unify Topological aspects (Thurston theory) and Complex analytical aspect (Ahlfors-Bers, Kodaira-Spencer theory). -
19:30
Conference Dinner, Restaurant le Petit Bois Vert (Petite France)
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Vendredi 9 juin 2017
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09:00
Valerii Berestovskii, Novosibirsk
On curvatures of homogeneous sub-Riemannian manifolds
Abstract: In the last years there arose an interest in definitions and calculations of sectional and Ricci curvatures of sub-Riemannian manifolds. For examples, one can mention recent papers of Agrachev-Barilari-Rizzi, Baudoin-Garofalo, Sturm, and others. I will discuss briefly some classical work papers connected with this subject by Schouten, Wagner, and especially a later paper by A.F.Solov'ev (1984) for rigged metrized distributions on Riemannian manifolds. To apply results of these papers, the author suggests to use in some cases special riggings of corresponding invariant bracket generated distributions on homogeneous sub-Riemannian manifolds. In particular, this method works for contact sub-Riemannian manifolds, sub-Riemannian Carnot groups, for horizontal distribution of natural submersion of full connected semisimple isometry group of Riemannian symmetric space onto this space. -
10:00
Coffee Break
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10:30
Daniele Alessandrini, Heidelberg
Geometric Structures with Quasi-Hitchin Holonomy
Abstract: I will describe some manifolds admitting parabolic geometric
structures whose holonomy is a Hitchin or a Quasi-Hitchin
representation. This generalizes the Thurston's theories of Fuchsian
and Quasi-Fuchsian representations to higher rank Lie groups. The
results come from a joint work with Qiongling Li and a joint work with
Sara Maloni and Anna Wienhard. -
11:30
Mahmoud Zeinalian, New York
On some symplectic aspects of moduli stack of Chen connections
The study of the Poisson geometry of the Teichmuller space and the moduli space of local systems gave rise to the discovery of the Goldman bracket of curves on an oriented surface which in turn led Chas and Sullivan to discover string topology operations on chains on the free loop space of an arbitrary oriented manifold. Their string topology operations also generalized the Turaev cobracket which did not come from a Poisson geometric origin, and the search for the geometric meaning of all string topology operations continues. In this direction, I will discuss some Poisson geometric aspects of the moduli stack of Z-graded Chen connections and how in the large N-limit an additional relevant structure should appear (N=dimension of the fibre). Unlike the Z-graded case, the somewhat conceptually different Z/2 graded case, studied several years ago with Hossein Abbaspour, did not require the use of derived geometry. The simple reason is that there are very few maps (e.g. traces) from a Z-graded object to a ground ring concentrated in degree zero, whereas in the Z/2 graded setting, viable maps exist. In the derived setting the single ground ring is replaced by the class of all non-positively graded differential graded algebras, with the differential going up towards the origin, as the test objects (i.e. a deformation functor). I plan to review the necessary background material before discussing recent work. This is part of a joint work in progress with Gregory Ginot and Owen Gwilliam. -
14:00
Francesco Bonsante, Pavia
The volume of the convex core of globally hyperbolic AdS space-times
Abstract: Globally hyperbolic AdS space-times are Lorentzian manifolds of constant curvature -1 with topological support the product of a surface and the real line. Once the genus of the surface is fixed, Mess showed that the relevant moduli space is the product of two copies of the Teichmüller space of the corresponding surface. In analogy with the quasi-Fuchsian case those Lorentzian manifolds contain a convex core. In the talk, after briefly revising the theory of GH AdS space-times, I will determine the coarse behavior of the volume of the convex core in terms of the L^1-energy between the two hyperbolic metrics associated to the space-time by Mess. This is a joint work with A. Seppi and A. Tamburelli. -
15:00
Coffee Break
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15:30
Rinat Kashaev, Genève
Teichmüller TQFT: old and new
Abstract: The Teichmüller TQFT is a combinatorial model of a three-dimensional TQFT of infinite type where the underlying vector spaces associated with surfaces are infinite dimensional. It is expected to be part of exact quantum Chern-Simons theory with non-compact gauge groups PSL(2,R) and PSL(2,C), the orientation preserving isometry groups in hyperbolic geometries in dimensions 2 and 3 respectively. There exist two versions of the Teichmüller TQFT called « old » and « new » formulations which are not equivalent in general but coincide when restricted to integer homology spheres. The talk is based on the works done in collaboration with Joergen Ellegaard Andersen. -
16:30
George Daskalopoulos, Providence
Rigidity of Group Actions on NPC Spaces
Abstract: The goal of this talk is to describe two different approaches of using harmonic maps into metric spaces of non-positive curvature in the sense of Alexandrov to prove rigidity. -
18:00
Reception, City hall (Mairie), Place Broglie
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Samedi 10 juin 2017
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09:00
Richard Wentworth, Maryland
Higgs bundles and pleated surfaces
Abstract: In this talk I will revisit the asymptotic structure of the SL(2,C) character variety of a closed surface group. Recent work of Taubes and Mazzeo, et.al. describes the large scale behavior of solutions to the Hitchin equations in terms of certain limiting configurations. I will show how these correspond, via harmonic maps, exactly to Bonahon's parametrization of pleated surfaces in hyperbolic 3-space by transverse and bending cocycles for a geodesic lamination. This is joint work with Andreas Ott, Jan Swoboda, and Mike Wolf. -
10:00
Coffee Break
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10:30
Gael Meigniez, Vannes
Thurston's Foliation Theorem in codimension 1, old and new
Abstract: In 1976, W. Thurston published two forms of the h-principle for foliations of codimension 1, on closed manifolds of all dimensions. I shall recall his methods and give some more recent improvements in ambiant dimension at least 4, avoiding the use of Mather's homology equivalence in the proof, and obtaining foliations with all leaves dense. -
11:30
Sumio Yamada, Tokyo
Harmonic map construction of 4+1 spacetimes with non-spherical blackholes
Abstract: Based on a collaborative project with Marcus Khuri and Gilbert Weinstein, we construct solutions to the 4+1 dimensional vacuum Einstein equation. We impose stationarity and two axisymmetries of the spacetime which would reduce the Einstein equation to a semi-linear elliptic system, which in turn is identified with the harmonic map equation into a symmetric space. In this construction, we obtain a whole new set of the solutions to the Einstein equation whose blackhole horizons have the entire range of topological types appearing as the irreducible elements in the prime decomposition theorem of three dimensional manifolds. -
12:30
End Of The Conference (a Drink)