Thursday, March 19, 2009 in Lunt 105
12:00pm
Pierre Schapira, University of Paris VI
Around Microlocalization
Microlocalization appears in different contexts: on real or complex manifolds, on contact, symplectic or Poisson manifolds. I will explain which are the natural objects in some cases (microdifferential operators, DQ-algebras, microlocal sheaves and their conjectural links with the Fukaya category (Nadler-Zaslow, Tamarkin).
2.30pm
David Treumann, University of Minnesota
The Coherent-constructible Correspondence for Toric Varieties
This is a talk on joint work with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow. It is in some sense a sequel to Bohan's March 10 talk, but I will try to keep it independent. I will discuss a triangle of equivalences we have constructed between a category of equivariant coherent sheaves on a toric variety, a category of polyhedrally-constructible sheaves on a real vector space, and a Fukaya category of Lagrangian branes in a symplectic vector space. Many famous results of toric geometry admit interpretations in terms of this coherent-constructible correspondence, and the connection to the Fukaya category can be seen as a verification - for toric varieties - of an equivariant form of Kontsevich's homological mirror symmetry conjectures.
4:00pm
Takuro Mochizuki, RIMS, Kyoto University
Wild Harmonic Bundles and Wild Pure Twistor D-modules
The study of wild harmonic bundles consists of three main parts:
(A) the asymptotic behaviour of wild harmonic bundles,
(B) an application to algebraic meromorphic flat bundles, or Higgs bundles,
(C) an application to wild pure twistor D-modules.
Then, in all, we obtain a nice application to algebraic holonomic D-modules.
