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# Résultats de recherche

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## Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 1)

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 ... Voir la vidéole (1h32m24s)

## Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 2)

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 ... Voir la vidéole (1h37m28s)

## François Lalonde - Applications of Quantum homology to Symplectic Topology (Part 1)

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 ... Voir la vidéole (1h22m28s)

## Alessandro Chiodo - Towards global mirror symmetry (Part 2)

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathe- matics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the introduction of new techniques, which are interesting in their own right. Among them, Gromov{Witten theory and its variants allow us to provide a re ned statement of mirror symmetry. Of course this leads to further open questions (despite much e ort and progress, Gromov{Witten theory ... Voir la vidéole (54m5s)

## Alessandro Chiodo - Towards global mirror symmetry (Part 1)

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the introduction of new techniques, which are interesting in their own right. Among them, Gromov{Witten theory and its variants allow us to provide are ned statement of mirror symmetry. Of course this leads to further open questions (despite much e ort and progress, Gromov{Witten theory remains unknown in high genus for the ... Voir la vidéole (1h27m36s)

## Alessandro Chiodo - Towards global mirror symmetry (Part 3)

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathe- matics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the introduction of new techniques, which are interesting in their own right. Among them, Gromov{Witten theory and its variants allow us to provide a re ned statement of mirror symmetry. Of course this leads to further open questions (despite much e ort and progress, Gromov{Witten theory ... Voir la vidéole (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 ... Voir la vidéole (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 ... Voir la vidéole (1h33m16s)