[geometry-ml:01203] Workshop on Geometry and Analysis of Discriminants 2/7-8 at IPMU

[Satoshi Kondo]

Dear colleagues:

There will be a workshop as follows at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

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

==========================================

                             Workshop
                                   on
        Geometry and Analysis of Discriminants

    IPMU (http://www.ipmu.jp/), 7-8 February, 2011

In the present workshop, we shall discuss several geometric, topological
and analytic aspects of discriminants and free divisors (thema includes:
fundamental groups of their compliments, uniformization and Gauss-Manin
equations, Fourier-Melin transforms of the solutions,..., etc). Anyone,
who is interested in, is welcome to participate the workshop.


Place:   IPMU Seminar Room A,
         Kashiwano-ha campus,
         the University of Tokyo

Access:   Following is an instruction from Tokyo station. It takes one hour.
        1. Take Tsukuba express from Akihabara and get out at Kashiwano-ha
           Campus station (around 30 minuites from Akihabara),
        2. Take Kashiwano-ha-Kouen Junkan Bus from west side of the station
           and get out at Kokuritsu gan center (less than 10 minuites),
        3. Walk to IPMU in the campus (less than 10 minuites).

Schedule:    13:30 February 7  ---  17:00 February 8, 2011
             Details of the program will be fixed later.

Organizers:  Kyoji Saito (the University of Tokyo)
             Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
             Kiyoshi Takeuchi (Tsukuba University)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
List of Participants:

T. Ishibe     (Dept. Math., Hiroshima Univ.) <chamarims ＠ yahoo.co.jp>

M. Kato      (Dept. Math., Univ. of Ryukyu)  <mkato ＠ edu.u-ryukyu.ac.jp>

T. Milanov  (IPMU, Univ. of Tokyo)  <todor.milanov ＠ ipmu.jp>

K. Saito     (IPMU, Univ. of Tokyo)  <kyoji.saito ＠ ipmu.jp>

J. Sekiguchi  (Dept. Math., Tokyo Univ. of Agriculture and Technology)
<sekiguchi ＠ cc.tuat.ac.jp>

S. Tajima    (Dept. Math., Tsukuba Univ.) <tajima ＠ math.tsukuba.ac.jp>

K. Takeuchi  (Dept. Math., Tsukuba Univ.）<takechan ＠ abel.math.tsukuba.ac.jp>

S. Tanabe  (Dept. Math., Galatasaray Univ.) <tanabesusumu ＠ hotmail.com>

K. Ueda   (Dept. Math., Osaka City Univ.) <uedakazushi ＠ gmail.com>

M. Yoshinaga  (Dept. Math., Kyoto Univ.) <mhyo ＠ math.kyoto-u.ac.jp>

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Titles and Abstracts:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Tadashi Ishibe

Title: Monoids in the fundamental groups of the complement of
logarithmic free divisors in $\C3$

Abstract：
We study monoids generated by certain Zariski-van Kampen generators in
the 17 fundamental groups of the complement of logarithmic free divisors
in $\C3$ listed by Sekiguchi. They admit positive homogeneous presentations.
Five of them are Artin monoids and eight of them are free abelian monoids.
The remaining four monoids are not Gau\ss ian and, hence, are neither
Garside nor Artin.  However, we introduce the concept of fundamental
elements for
positive homogeneously presented monoids, and show that all 17 monoids
possess fundamental elements.  As an application of the study of monoids,
we solve some decision problems for the fundamental groups except three cases.
(joint work with Kyoji Saito)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Jiro Sekiguchi

Title: Saito free divisors in a four dimensional affine space

Abstract:
There is a relationship between Saito free divisors in ${\bf C}3$
defined by weighted homogeneous polynomials and 1-parameter
equisingular deformations of isolated curve singularities.
This idea leads us to find several examples of Saito free divisors in
${\bf }3$ including disciriminants of complex reflection groups of rank three.
This kind of phenomena seem  not occur in higher dimensional case.
The speaker reports in this talk an idea to construct Saito free divisors
in ${\bf C}4$ and discuss a comparison of such divisors
with discriminants of complex reflection groups of rank four.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Shin-ichi Tajima

Title: $\mu$-constant deformations and algebraic local cohomology

Abstract:
We study $\mu$-constant deformations for semi-quasihomogeneous
hypersurface isolated singularities by using the Grothendieck local
duality.
We present a new method for computing Tjurina stratifications of $
\mu$-constant deformations. The key ingredient in this approach is the
concept of parametric algebraic local cohomology.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Kiyoshi Takeuchi

Title: Motivic Milnor fibers and Jordan normal forms
of monodromies (joint work with Y. Matsui and
A. Esterov)

Abstract:
By computing the equivariant mixed Hodge numbers of motivic Milnor
fibers introduced by Denef-Loeser etc., we obtain various formulae
for the Jordan normal forms of the local and global monodromies of
polynomials.  For polynomials over affine complete intersection
varieties the results will be described by the mixed volumes of the
faces of their Newton polyhedrons.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Susumu Tanabe

Title: Hodge structure of  period integrals revisited.

Abstract:
Several years ago I proposed a method to calculate Mellin transform of
period integrals defined for a certain class of affine complete
intersection varieties.
As a result of calculus, it turns out that the mixed Hodge structure of the
variety reflects on the arrangement of poles of Mellin transform of  period
integrals.  Almost at the same period,  papers by Douai-Sabbah appeared.
There the authors establish the existence of  Kashiwara-Malgrange filtration
for a D-module associated to the oscillatory integrals defined on an affine
algebraic hypersurface.  I would like to discuss the relation between
these two approaches to the Hodge structure of integrals.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Kazushi Ueda

Title: Mirror symmetry and Calabi-Yau hypersurfaces in weighted
projective spaces

Abstract:
Based on joint works with Masahiro Futaki, Akira Ishii and Susumu Tanabe,
I will discuss relations between

1. HMS (homological mirror symmetry) for weighted projective spaces,
2. HMS for Calabi-Yau Fermat hypersurfaces in weighted projective spaces,
3. HMS for Brieskorn-Pham singularities, and
4. monodromy of certain hypergeometric functions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Masahiko Yoshinaga

Title: Minimal stratification for line arrangements and
presentations of fundamental groups

Abstract:
The fundamental group of the complements to line arrangements
has minimal presentation. This fact has been generalized to "the
minimality of the complement of hyperplane arrangements".
Recently several descriptions of minimal CW complexes appear.
In this talk, I would like to talk about "minimal stratification" which
can be considered as a dual object to minimal CW complex and
also discuss associated presentations of fundamental groups.

=================================================
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/