I plan to discuss the way to construct such spaces Is geometry of deformed Calabi-Yau manifolds (a kind of deformation There is another kind of non-commutative geometry of Mirror Symmetry. I am going toĮxplain non-commutative formal geometry of those homotopy categories. On the algebraic side we will meet homotopyĬategories associated with compact symplectic manifolds. Mirror symmetry can be explained in terms of the residualĬommutative geometry. Such non-commutative spaces can degenerate “at Suggest to view a given Conformal Field Theory as a kind of Mathematical idea of Gromov-Hausdorff collapse of Calabi-Yau manifolds,Īs well as with unexpected relation to rigid analytic geometry. It combines physical idea of degenerating Conformal Field Theories with Non-commutative geometry provides anĪppropriate framework for study of what is called “D-branes” in the Questions of algebraic and symplectic geometry, algebra, number theoryĪnd differential equations. String theories, Mirror Symmetry turned out to be related to many deep Discovered by physicists as a duality on a certain class of Mirror Symmetry in terms of homological algebra and non-commutative He will explain the approach to Mirror Symmetry suggested in a joint To save some time, as an introduction I simply quote the following summary from a lecture Soibelman has given last October at Vanderbilt University
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