January 24-29, 2011, University of Miami

**Mark Gross** (UC San Diego):
Theta functions for K3 surfaces and tropical Morse trees.

**Maxim Kontsevich** (IHES and U. Miami):
Classical and quantum geometry of integrable systems

**Naichung Conan Leung** (Chinese Univ. of Hong Kong):
SYZ mirror symmetry

**Andrew Neitzke** (U. Texas Austin):
A construction of hyperkahler metrics, with application to Hitchin systems

**Pierre Schapira** (Institut de Mathématiques de Jussieu):
Microlocal theory of sheaves and applications to non-displaceability

In the first talk we will explain the main notions and results of the microlocal theory of sheaves: the microsupport of sheaves and its behaviour with respect to the 6 operations, with emphasis on the Morse lemma.

In the second talk, inspired by the recent work of Tamarkin but with really different methods and results, we will apply these tools to treat some problems of non-displaceability, including the conservation of Morse inequalities as well as some results specific to positive isotopies. The main tool is a theorem which asserts that any Hamiltonian isotopy admits a unique sheaf quantization (joint work with S. Guillermou and M. Kashiwara).

References:-
M. Kashiwara and P. Schapira,
*Sheaves on Manifolds,*Grundlehren der Math. Wiss.**292**Springer-Verlag (1990). -
S. Guillermou, M. Kashiwara and P. Schapira,
*Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems,*math.arXiv:1005.1517 -
D. Tamarkin,
*Microlocal conditions for non-displaceability,*math.arXiv:0809.1584

**Mohammed Abouzaid** (Clay Institute and MIT):
Homotopy equivalence of nearby Lagrangians

**Matthew Ballard** (U. Penn.):
Orlov spectra

**Thomas Kragh** (MIT):
Nearby Lagrangians with arbitrary Maslov class.

**Dmitri Orlov** (Steklov Institute):
D-branes in LG-models, matrix factorizations, and triangulated
categories
of singularities: properties and relations.

**Tony Pantev** (U. Penn.):
Mirror symmetry and mixed Hodge structures

**James Pascaleff** (MIT):
Floer cohomology in the mirror of CP^2 relative to a conic and a line

**Nick Sheridan** (MIT):
On the Homological Mirror Symmetry conjecture for pairs of pants

**Bernd Siebert** (Univ. Hamburg):
Logarithmic Gromov-Witten invariants

**Yan Soibelman** (Kansas State U.):
Complex integrable systems, wall-crossing formulas and Calabi-Yau
categories

**David Treumann** (Northwestern):
Plumbings, constructible sheaves, and HMS