Objetivo 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. Ámbito científico natural sciencesmathematics Palabras clave hodge conjecture mirror symmetry rationality Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Convocatoria de propuestas ERC-2008-AdG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-AG - ERC Advanced Grant Institución de acogida UNIVERSITAT WIEN Aportación de la UE € 1 060 800,00 Dirección UNIVERSITATSRING 1 1010 Wien Austria Ver en el mapa Región Ostösterreich Wien Wien Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Helmut Schaschl (Dr.) Investigador principal Ludmil Katzarkov (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo UNIVERSITAT WIEN Austria Aportación de la UE € 1 060 800,00 Dirección UNIVERSITATSRING 1 1010 Wien Ver en el mapa Región Ostösterreich Wien Wien Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Helmut Schaschl (Dr.) Investigador principal Ludmil Katzarkov (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos