**Title:** Special Lagrangian Submanifolds in Mirror Symmetry

**Speaker:** Sema Salur

**Speaker Info:** Cornell University

**Brief Description:**

**Special Note**:

**Abstract:**

String theorists believe that every Calabi-Yau 3-fold X has a quantization, which is a Super Conformal Field Theory (SCFT) - a Hilbert space H with a collection of operators satisfying some relations - to be interpreted as the quantum theory of strings moving in X. Two different Calabi-Yau manifolds X and X' may have the same SCFT and in this case there are powerful relationships between the (topological) invariants of X and X'. This is the idea behind the Mirror Symmetry.Even though there is no good mathematical definition of the relationship between conformal field theories and the Calabi-Yau 3-folds, there are now two conjectural theories (due to Kontsevich and Strominger-Yau-Zaslow) which explain the Mirror Symmetry in a mathematical way.

In this talk, I will first give brief introductions to Calabi-Yau manifolds and special Lagrangian submanifolds, and then a short survey of my research about local geometric approach to SYZ conjecture.

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