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Nombre de programmes trouvés : 16962
Cours magistraux

le (1h25m16s)

Alexandre Sukhov - J-complex curves: some applications (Part1)

We will focus in our lectures on the following : 1. J-complex discs in almost complex manifolds : general properties. Linearization and compactness. Gromov’s method : the Fredholm alternative for the d-bar operator. Attaching a complex disc to a Lagrangian manifold. Application : exotic symplectic structures. Hulls of totally real manifolds : Alexander’s theorem. 2. Real surfaces in (almost) complex surfaces. Filling real 2-spheres by a Levi-flat hypersurface (Bedford -Gaveau-Gromov theorem). Some applications. Symplectic and contact structures. Reeb foliation and the Weinsten conjecture. Hofer’s proof of ...
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Cours magistraux

le (1h34m53s)

François Lalonde - Applications of Quantum homology to Symplectic Topology (Part 2)

The first two lectures will present the fundamental results of symplectic topology : basic definitions, Moser’s lemma, normal forms of the symplectic structure near symplectic and Lagrangian submanifolds, characterization of Hamiltonian fibrations over any CW-complex. The third course will give the application of quantum homology to the splitting of the rational cohomology ring of any Hamiltonian fibration over S2, a generalization of a result of Deligne in the algebraic case and of Kirwan in the toric case. The fourth course will give the ...
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Cours magistraux

le (1h33m16s)

François Lalonde - Applications of Quantum homology to Symplectic Topology (Part 3)

The first two lectures will present the fundamental results of symplectic topology : basic definitions, Moser’s lemma, normal forms of the symplectic structure near symplectic and Lagrangian submanifolds, characterization of Hamiltonian fibrations over any CW-complex. The third course will give the application of quantum homology to the splitting of the rational cohomology ring of any Hamiltonian fibration over S2, a generalization of a result of Deligne in the algebraic case and of Kirwan in the toric case. The fourth course will give the ...
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Cours magistraux

le (1h33m15s)

François Lalonde - Applications of Quantum homology to Symplectic Topology (Part 4)

The first two lectures will present the fundamental results of symplectic topology : basic definitions, Moser’s lemma, normal forms of the symplectic structure near symplectic and Lagrangian submanifolds, characterization of Hamiltonian fibrations over any CW-complex. The third course will give the application of quantum homology to the splitting of the rational cohomology ring of any Hamiltonian fibration over S2, a generalization of a result of Deligne in the algebraic case and of Kirwan in the toric case. The fourth course will give the ...
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Cours magistraux

le (1h37m52s)

Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 3)

This series of lectures is dedicated to recent results concerning the existence of holomorphic curves on the surfaces of class VII. The first lecture will be an introduction to the Donaldson theory. We will present the fundamental notions and some important results in the theory, explaining ideas of the proofs. In the second lecture we will present the theory of holomorphic fiber bundles on complex surfaces, the stability notion, moduli spaces and the Kobayashi-Hitschin correspondence that links moduli spaces of stable fiber bundles (defined ...
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Cours magistraux

le (1h13m40s)

Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 4)

This series of lectures is dedicated to recent results concerning the existence of holomorphic curves on the surfaces of class VII. The first lecture will be an introduction to the Donaldson theory. We will present the fundamental notions and some important results in the theory, explaining ideas of the proofs. In the second lecture we will present the theory of holomorphic fiber bundles on complex surfaces, the stability notion, moduli spaces and the Kobayashi-Hitschin correspondence that links moduli spaces of stable fiber bundles (defined ...
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Conférences

le (50m2s)

Robert Haslhofer - The moduli space of 2-convex embedded spheres

We investigate the topology of the space of smoothly embedded n-spheres in R^{n+1}, i.e. the quotient space M_n:=Emb(S^n,R^{n+1})/Diff(S^n). By Hatcher’s proof of the Smale conjecture, M_2 is contractible. This is a highly nontrivial theorem generalizing in particular the Schoenflies theorem and Cerf’s theorem.In this talk, I will explain how geometric analysis can be used to study the topology of M_n respectively some of its variants.I will start by sketching a proof of Smale’s theorem that M_1 is contractible. By a beautiful theorem of Grayson, the curve shortening flow deforms any closed embedded curve in the plane to a round circle, ...
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Conférences

le (1h4m1s)

Feng Luo - Discrete conformal geometry of polyhedral surfaces and its convergence

Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces.   In this talk, we prove that discrete uniformizaton maps converge to conformal maps when the triangulations are sufficiently fine chosen.  We will also discuss the relationship between the discrete uniformization theorem and convex polyhedral surfaces  in the hyperbolic 3-space.  This is a joint work with J. Sun and T. Wu.
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Conférences

le (51m50s)

Melanie Rupflin - Horizontal curves of metrics and applications to geometric flows

On closed surfaces there are three basic ways to evolve a metric, by conformal change, by pull-back with diffeomorphisms and by horizontal curves, moving orthogonally to the first two types of evolution. As we will discuss in this talk, horizontal curves are very well behaved even if the underlying conformal structures degenerate in moduli space as t to T. We can describe where the metrics will have essentially settled down to the limit by time t T as opposed to regions on which the metric still has to do an infinite amount of stretching. This quantified information is essential in ...
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