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Generalized Homological Mirror Symmetry and Applications

Objectif

Mirror symmetry arose originally in physics, as a duality between $N = 2$ superconformal field theories. Witten formulated a more mathematically accessible version, in terms of topological field theories. Both conformal and topological field theories can be defined axiomatically, but more interestingly, there are several geometric ways of constructing them. A priori, the mirror correspondence is not unique, and it does not necessarily remain within a single class of geometric models. The classical case relates $\sigma$-models, but in a more modern formulation, one has mirror dualities between different Landau-Ginzburg models, as well as between such models and $\sigma$-models; orbifolds should also be included in this. The simplest example would be the function $W: \C \rightarrow \C$, $W(x) = x^{n+1}$, which is self-mirror (up to dividing by the $\bZ/n+1$ symmetry group, in an orbifold sense). While the mathematics of the $\sigma$-model mirror correspondence is familiar by now, generalizations to Landau-Ginzburg theories are only beginning to be understood. Today it is clear that Homologcal Mirror Symmetry (HMS) as a categorical correspondence works and it is time for developing direct geometric applications to classical problems - rationality of algebraic varieties and Hodge conjecture. This the main goal of the proposal. But in order to attack the above problems we need to generalize HMS and explore its connection to new developments in modern Hodge theory. In order to carry the above program we plan to further already working team Vienna, Paris, Moscow, MIT.

Champ scientifique

Appel à propositions

ERC-2008-AdG
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Régime de financement

ERC-AG - ERC Advanced Grant

Institution d’accueil

UNIVERSITAT WIEN
Contribution de l’UE
€ 1 060 800,00
Adresse
UNIVERSITATSRING 1
1010 Wien
Autriche

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Région
Ostösterreich Wien Wien
Type d’activité
Higher or Secondary Education Establishments
Contact administratif
Helmut Schaschl (Dr.)
Chercheur principal
Ludmil Katzarkov (Prof.)
Liens
Coût total
Aucune donnée

Bénéficiaires (1)