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Cours magistraux

le (1h18m12s)

Serguei Ivachkovitch - Method of pseudoholomorphic curves and applications (Part 4)

The method of « pseudoholomorphic » curves proved itself to be extremely useful in different fields. In symplectic topology, for instance Gromov’s Nonsqueezing Theorem, Arnold’s conjecture and the Floer homology, the Gromov-Witten invariants. In complex analysis and geometry, for instane polynomial hulls of totally real surfaces, envelopes of meromorphy, holomorphic foliations. We shall develop the theory of complex curves in almost complex manifolds and discuss some of these applications in our lectures.
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Cours magistraux

le (1h31m0s)

Claude Viterbo - Théorie des faisceaux et Topologie symplectique (Part 1)

L’utilisation de méthodes de théorie des faisceaux (Kashiwara-Schapira)a été dévelopée ces dernières années par Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara et Schapira. Nous essaierons d’en donner un aperçu à la fois pour démontrer des résultats classiques, comme la conjecture d’Arnold, et pour des résultats nouveaux. The use of methods from the Sheaf Theory (Kashiwara-Schapira) was developped recently by Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara and Schapira. We will try to give an insight of that, in order to prove classical results, such as ...
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Cours magistraux

le (1h34m32s)

Claude Viterbo - Théorie des faisceaux et Topologie symplectique (Part 3)

L’utilisation de méthodes de théorie des faisceaux (Kashiwara-Schapira)a été dévelopée ces dernières années par Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara et Schapira. Nous essaierons d’en donner un aperçu à la fois pour démontrer des résultats classiques, comme la conjecture d’Arnold, et pour des résultats nouveaux. The use of methods from the Sheaf Theory (Kashiwara-Schapira) was developped recently by Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara and Schapira. We will try to give an insight of that, in order to prove classical results, such as ...
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Conférences

le (1h30m3s)

Rahul Pandharipande - Stable quotients and relations in the tautological ring

The topic concerns relations among the kappa classes in the tautological ring of the moduli space of genus g curves. After a discussion of classical constructions in Wick form, we derive an explicit set of relations obtained from the virtual geometry of the moduli space of stable quotients. In a series of steps, the stable quotient relations are transformed to simpler and simpler forms. Our nal result establishes a previously conjectural set of tautological relations proposed a decade ago by Faber{Zagier.
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Cours magistraux

le (1h37m8s)

Yuan-Pin Lee - Introduction to Gromov-Witten theory and the crepant transformation conjecture (Part 2)

In these lectures, Gromov{Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be explained. Some examples, with emphasis on the projective/global cases, will be given. Note: The construction of virtual fundamental class, which forms the foundation of the GW theory, will be given in Jun Li's concurrent lectures and will not be explained here.
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Conférences

le (52m31s)

Aaron Pixton - The stable pairs equivariant descendent vertex

The counting function associated to the moduli space of stable pairs on a 3-fold X is conjectured to give the Laurent expansion of a rational function. For toric X , this conjecture can be proven by a careful grouping of the box con gurations appearing in the stable pairs equivariant descendent vertex. I will describe this approach and then say a little about how it might also be used to study the Donaldson{Thomas vertex. This talk presents joint work with Rahul Pandharipande.
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