[geometry-ml:02337] FMSP-IPMU special lectures -- Tomoyuki Mano (Ryuukyu university) -- April 24, 2015

[Todor Milanov]

Dear all,

I would like to forward the following announcement

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以下の要領でFMSP-IPMU特別セミナーを開催しますのでご案内致します。
                                   世話人:　河野俊丈、斎藤恭司

日時：　2015年　4月24日(金）10:30-12:00、13:30-15:00、15:30-17:00
場所：　IPMU　4階、　バルコニー　A
講師：　眞野智行　（琉球大学）
表題：　アイソモノドロミー変形空間上の平坦構造

アブストラクトは以下の英語表示をご覧下さい。

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We shall have a FMSP-IPMU special seminar as follows.

Speaker:   Tomoyuki Mano   (Ryuukyu university)
　Title:   Flat structure on isomonodormic deformations
　 Date:   Fri, April 24, 2015, 10:30-12:00, 13:30-15:00, 15:30-17:00
  Place:   Balcony A,  IPMU

Abstract: The WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equation was
found by physicists in 2D topological field theory. B. Dubrobin proved
by introducing the notion of Frobenius manifolds that there exists a
correspondence between solutions to the WDVV equation and isomonodromic
deformations of linear differential equations with special conditions.
(In n=3 case, the (n=3) WDVV equation is equivalent to a one-parameter
family of the sixth Painleve equations.) The main purpose of this talk
is to generalize the WDVV equation so that the generalized equation will
be equivalent to isomonodromic deformations of generic linear
differential equations of Okubo type. I will also show the existence of
a "flat generator systems" of invariant polynomials for the standard
action of a finite complex reflection group. This is a generaliztion of
K. Saito's result for finite Coxeter groups.
 The talk will proceed along the following line: 1. I will introduce a
completely integrable system of differential equations of Okubo type in
several variables and explain some basic facts about logarithmic vector
fields along a divisor. 2. I will introduce a geometric structure called
"Saito structure without metric" which is presented in C. Sabbah's
textbook. 3. I will show that it is possible to construct a Saito
structure without metric on the space of the independent variables of a
generic Okubo type system in several variables. The existence of flat
generator systems for finite complex reflection groups is a consequence
of this construction.

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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov ＠ ipmu.jp