|Speaker:||Dmitry Tamarkin (Northwestern University)|
|Title:||Microlocal condition for non-displaceability of Lagrangian submanifolds.|
|Date:||Fri, Nov 27, 2009, 17:00 - 18:30|
|Place:||Seminar Room at IPMU Prefab. B|
Consider a cotangent bundle T^*X viewed as a symplectic manifold. Consider a subgroup G of symplectomorphisms of T^*X generated by flows of compactly supported Hamiltonians. Subsets A,B of T^*X are called non-displaceable if for any g in G, the shifted set g.A intersects B. If A and B are Lagrangian submanifolds then the sufficient condition for non-displaceability is vanishing of Floer cohomology.
I will give an alternative sufficient condition which is based on Kashiwara-Schapira's notions of microsupport.
This condition works in some non-trivial cases.
A key ingredient of this condition is a certain full subcategory of the derived category of sheaves of vector spaces on X\times R (R is the real line). This category has similar properties to the Fukaya category of T^*X.