Microlocal Miniconference

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.

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