Workshop on Geometry and Nonlinear PDE

日時：2015 年1月13日（火）14：45〜18：20
場所：早稲田大学西早稲田キャンパス51号館18階06室
http://www.waseda.jp/top/access/nishiwaseda-campus}

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2015年1月13日（火）

14：45〜15：45　Chang-Shou Lin (National Taiwan University)
Mean field equations, isomonodromic deformation and Painleve VI

16:00〜17:00　 Martin Guest (Waseda University)
Painleve III: the geometry of the solutions

17：20〜18：20　Takashi Takebe（Higher School of Economics, Moscow）
Dispersionless integrable hierarchies and Loewner equations

18：40〜　懇親会

講演要旨

Chang-Shou Lin (National Taiwan University)
Title: Mean field equations, isomonodromic deformation and Painleve VI
Abstract:
Recently we discovered the connection of bubbling phenomena with
solutions of Painleve VI.
I will talk about this connection and other developments.

Martin Guest(Waseda University)
Title: Painleve III: the geometry of the solutions
Abstract:
This is part of a project to study nonlinear pde related to
geometry/physics,
by using integrable systems methods as well as pde methods.
In this talk we use the radial sinh-Gordon equation (Painleve III
equation) as a basic example.
By combining local and global information, we build a complete picture
of the behaviour of all solutions.
This is joint work with Claus Hertling (University of Mannheim).

Takashi Takebe（Higher School of Economics, Moscow）
Title: Dispersionless integrable hierarchies and Loewner equations
Abstract:
Dispersionless integrable hierarchies are a class of integrable systems
obtained
as quasi-classical limits of integrable hierarchies like the KP hierarchy,
the Toda lattice hierarchies and so on.
It turned out that Loewner type equations in complex analysis appear
from the reduction of dispersionless
integrable hierarchies.
Examples of this phenomenon are presented.

この研究集会は, 日本学術振興会科学研究費 基盤研究(A)課題番号25247005
「Systematic development and application of methods in differential geometry
and integrable systems motivated by quantum cohomology」（代表 Martin　Guest）
及び
早稲田大学重点研究機構「非線形偏微分方程式研究所」
の援助を受けています.

組織員
Martin Guest（早稲田大学理工学術院）
小澤徹　（早稲田大学重点研究機構「非線形偏微分方程式研究所」）
田中和永（早稲田大学重点研究機構「非線形偏微分方程式研究所」）
小薗英雄（早稲田大学重点研究機構「非線形偏微分方程式研究所」）