**Title:** Microlocal criterion for non-displaceability of Lagrangians

**Speaker:** Dmitry Tamarkin

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

Let L be a compact Lagrangian submanifold in T^*X. We then produce a full subcategory C_L in the category of sheaves on X\times R (R is the real axis). Given two Lagrangians L_1,L_2, take arbitrary objects F_1 from C_{L_1} and F_2 from C_{L_2}. One can define Rhom(F_1,F_2) as an object of the derived category of sheaves on R (because R acts on X\times R by shifts). Furthermore, one can define a map from Rhom(F_1,F_2) to its shift along R by any positive number. We prove that as long as this map is non-zero for all shifts, any hamiltonian shift of L_2 intersects L_1 (i.e. L_1 and L_2 are non-displaceable)As an application, we prove that the Clifford torus in CP^n is non-displaceable as well as the Clifford torus and RP^n

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