Dear colleagues:

We announce once again the following miniworkshop at IPMU
(the Institute for the Physics and Mathematics of the Universe).
It was previously announced 11/16-17 but we extend it:
11/16-18 with two more speakers.

Regards,

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

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Workshop on Recent Advances in Mathematics at IPMU

Date:   Nov. 16-18, 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

18 November (We)
13:30 - 15:30      Colin Ingalls
15:30 - 17:00      Timothy Logvinenko

***** 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: On the coarse geometry of Teichmueller space
Abstract: We discuss the synthetic geometry of the
    pants graph in comparison with the Weil-Petersson
    metric, whose geometry the pants graph coarsely
    models following work of Brock’s. We also restrict
    our attention to the pants graph of the 5-holed sphere,
    studying the Gromov bordification and the dynamics
    of pseudo-Anosov mapping classes.

Colin Ingalls
Title:  Rationality of the Brauer-Severi Varieties of Skylanin algebras
Abstract:  Iskovskih's conjecture states that a conic bundle over
    a surface is rational if and only if the surface has a pencil of
    rational curves which meet the discriminant in 3 or fewer points,
    (with one exceptional case).  We generalize Iskovskih's proof that
    such conic bundles are rational, to the case of projective space
    bundles of higher dimension.  The proof involves maximal orders
    and toric geometry.  As a corollary we show that the Brauer-Severi
    variety of a Sklyanin algebra is rational.

Timothy Logvinenko
Title: Derived functors between cotangent bundles of flag varieties
Abstract: This is a joint work with Rina Anno (UChicago). We construct a network
    of functors, which correspond to `generalized braid diagrams', between
    derived categories of coherent sheaves on cotangent bundles of full
    and partial flag varieties. We then prove that isotopic braid
    diagrams correspond to isomorphic functors. This generalises the
    classic braid group action of Khovanov-Thomas on a derived category of
    the cotangent bundle of a complete flag variety.
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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/