Geometry/Physics Seminar

Title: Microlocal criterion for non-displaceability of Lagrangians
Speaker: Dmitry Tamarkin
Speaker Info: Northwestern University
Brief Description:
Special Note:

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

Date: Thursday, February 7, 2008
Time: 4:00pm
Where: Lunt 107
Contact Person: Prof. Gabriel Kerr
Contact email: gdkerr@math.northwestern.edu
Contact Phone: 773-936-6405
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