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# Documents  Funar, Louis | enregistrements trouvés : 7

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## Which geodesic flows are left-handed? Dehornoy, Pierre | CIRM H

Post-edited

Research talks;Dynamical Systems and Ordinary Differential Equations;Topology

Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot
Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows ...

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## Braids and Galois groups Matzat, B. Heinrich | CIRM

Post-edited

Research talks;Algebraic and Complex Geometry;Number Theory;Topology

arithmetic fundamental group - Galois theory - braid groups - rigid analytic geometry - rigidity of finite groups

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## Quantum symmetry of conformal blocks andrepresentations of braid groups at roots of unity Kohno, Toshitake | CIRM

Multi angle

Research talks;Geometry;Topology

braid groups - conformal blocks - KZ equation - quantum group symmetry - hypergeometric integrals - Gauss-Manin connection

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## Precise statistical properties of the geodesic flow on periodic hyperbolic manifolds Thomine, Damien | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations

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## Logarithms and deformation quantization Alekseev, Anton | CIRM

Multi angle

Research talks;Algebra;Geometry

We prove the statement$/$conjecture of M. Kontsevich on the existence of the logarithmic formality morphism $\mathcal{U}^{log}$. This question was open since 1999, and the main obstacle was the presence of $dr/r$ type singularities near the boundary $r = 0$ in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at the boundary which implies the formality property of $\mathcal{U}^{log}$. We also show that the logarithmic formality morphism admits a globalization from $\mathbb{R}^{d}$ to an arbitrary smooth manifold. We prove the statement$/$conjecture of M. Kontsevich on the existence of the logarithmic formality morphism $\mathcal{U}^{log}$. This question was open since 1999, and the main obstacle was the presence of $dr/r$ type singularities near the boundary $r = 0$ in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise ...

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## Faithful actions of Gal($\mathbb{\bar{Q} /Q}$) and change of fundamental group Bauer, Ingrid C. | CIRM

Multi angle

Research talks;Algebraic and Complex Geometry;Number Theory

hyperelliptic curves - Belyi functions - absolute Galois group - Belyi polynomials - marked varieties - moduli spaces

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## Automorphisms of curve and pants complexes in profinite content Funar, Louis | CIRM H

Multi angle

Research talks;Algebra;Geometry;Algebraic and Complex Geometry;Topology

Pants complexes of large surfaces were proved to be vigid by Margalit. We will consider convergence completions of curve and pants complexes and show that some weak four of rigidity holds for the latter. Some key tools come from the geometry of Deligne Mumford compactification of moduli spaces of curves with level structures.

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