[geometry-ml:00957] Miniworkshop at IPMU 11/16-17

[Satoshi Kondo]

Dear colleagues:

We announce the following miniworkshop at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/

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Workshop on Recent Advances in Mathematics at IPMU

Date:   Nov. 16-17, 2009
Place:  Seminar Room at IPMU Prefab B
Organizing Committee:  Alexey Bondal and Kyoji Saito

Program:

16 November (Mo)
 9:45 - 10:45     Yuichi Nohara
11:00 - 12:00     Sergei Galkin
14:00 - 15:00     Alex Bene
15:30 - 16:30     Alexander Getmanenko

17 November (Tu)
 9:45 - 10:45     Tathagata Basak
11:00 - 12:00     Paul Bressler
14:00 - 15:00     Mikael Pichot
15:30 - 16:30     Ken Shakleton


***** Title and Abstract of Talks *****

Yuichi Nohara:
Title: Toric degenerations of Gelfand-Cetlin systems
       and potential functions
Abstract: It is well known that a polarized toric variety is
       related to a moment polytope in two different ways,
       monomial basis and the moment map. In the case of flag manifolds,
       certain polytopes, called Gelfand-Cetlin polytopes, also appear
       in similar ways: the Gelfand-Cetlin basis, a basis of an
       irreducible representation; and the Gelfand-Cetlin system,
       a completely integrable system. Furthermore the flag manifold
       admits a degeneration into a toric variety corresponding to
       the Gelfand-Cetlin polytope. Kogan and Miller proved that
       the Gelfand-Cetlin basis can be deformed into monomial basis
       on the toric variety under the degeneration.
       We show that the Gelfand-Cetlin system can be deformed into
       a moment map on the toric variety. We also apply the result
       to disk counting and calculate the potential function for a
       Lagrangian torus fiber of the Gelfand-Cetlin system.
       This is a joint work with T. Nishinou and K. Ueda.

Sergei Galkin:
Ttitle: Landau-Ginzburg models of Fano varieties
Abstract: TBA

Alex Bene:
Ttitle: Feynman diagrams and mapping class representations.
Abstract: In this talk, I will review how elementary moves on fatgraphs,
     a type of Feynman diagram with cyclically oriented vertices
     arising in 2D quantum gravity, defines the so-called Ptolemy
groupoid, which
     can be viewed as an enlargement of the mapping class group of a
     bordered surface.  This viewpoint allows for the possibility of
     certain mapping class representations to be "extended to the groupoid
     level."  I will discuss examples of such representations which have
     target a certain vector space generated by similar Feynman diagrams
     called Jacobi diagrams which have arisen in the field of finite type
     invariants and Chern-Simons theory.

Alexander Getmanenko:
Title: Towards proving existence of resurgent solutions of a linear ODE.
Abstract: The talk will be devoted to discussion of foundational issues
     in the mathematically rigorous hyperasymptotic, or
     "resurgent",theory of linear differential equations. We will look at
     Shatalov-Sternin's proof of existence of resurgent  solutions of a
     linear ODE and discuss the construction of analytic continuation to a
     common "Riemann surface'' of all terms of the von Neumann
     series appearing in their proof. A more modest statement will be
     presented that we could write up in a detailed and rigorous fashion.
     We will also mention possible applications of the theory.

Reference: arXiv:0907.2934

Tathagata Bassak:
Title: TBA

Paul Bressler:
Title: Deformations of gerbes

Mikael Pichot:
Title: Groups of intermediate rank.
Abstract: I will introduce countable
       discrete groups which interpolate
       the classical (integer) values of the
       rank, especially between rank 1
       and rank 2. This is joint work with
       S. Barre.

Ken Shakleton
Title: TBA
===========================

You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png

The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/