User yaniel cabrera - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T06:31:00Z http://mathoverflow.net/feeds/user/6527 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/43237/generalized-geometry Generalized geometry Yaniel Cabrera 2010-10-22T21:40:40Z 2012-09-28T08:38:36Z <p>What role do generalized geometries (in terms of Dirac structures, for instance, symplectic, Poisson, complex, and generalized complex structures in the sense of Hitchin, Cavalcanti, and Gualtieri) play in string theory?</p> <p>EDIT: More generally, what role to Dirac structures (subbundles of the generalized tangent bundle $TM \bigoplus T^*M$ which are maximally isotropic to the natural pairing and closed under the Courant bracket) play?</p> http://mathoverflow.net/questions/44900/mirror-symmetries-for-generalized-geometries Mirror symmetries for generalized geometries ? Yaniel Cabrera 2010-11-05T00:27:43Z 2010-11-05T15:52:38Z <p>For Calabi-Yau three-folds we have $\mathcal{mirror \ symmetry}$: a map that associates most Calabi-Yau three-folds $M$ another Calabi-Yau three-fold $W$ such that $h^{1,1}(M) = h^{2,1}(W)$ and $h^{1,1}(W) = h^{2,1}(M)$ where $h^{i,j}$ are the Hodge numbers of the Calabi-Yau. In string theory such a duality leads to the conjecture that the type IIA superstring theory compactified on $M$ is equvilalent to the type IIB compactified on $W$. </p> <p>$\textbf{Question} :$ Are there extensions of mirror symmetry applied to generalized geometries (in the sense of Hitchin, Cavalcanti, and Gualtieri)? If so, what is the state of the art of this topic/question?</p> http://mathoverflow.net/questions/43237/generalized-geometry Comment by Yaniel Cabrera Yaniel Cabrera 2010-10-22T23:19:15Z 2010-10-22T23:19:15Z @both: if generalized complex structures are different from generalized geometries, then my question refers to generalized geometries. The type described in the comment right above this one. And yes David MJC, feel free to elaborate! http://mathoverflow.net/questions/43237/generalized-geometry Comment by Yaniel Cabrera Yaniel Cabrera 2010-10-22T22:46:32Z 2010-10-22T22:46:32Z yes, the updated version is clearer. thanks.