Workshop on:

Isomonodromic deformations and related topics

Place Date Topics Format

Waseda University

Nishi-Waseda Campus

Building 51, 18th Floor, Room 18-02

Nishi-Waseda Campus access map

Map showing building 51

 

22 November

(Fri)

-23 November

(Sat)

2013

Isomonodromic deformations,

mirror symmetry,

etc

Workshop

Organisers: Martin Guest (Waseda University) and Masa-Hiko Saito (Kobe University)

Supported by JSPS Grant-in-Aid for Scientific Research (S)24224001 (PI: Masa-Hiko Saito) and Waseda University Grant for Special Research Project 2013B-083 (PI: Martin Guest)


PROGRAM


Friday 22 November

15:00-16:00 Shinobu Hosono (Tokyo University) "Differential rings over the moduli spaces of Calabi-Yau manifolds II"

Abstract: I will discuss certain differential rings over the moduli spaces and try to see the structure of the so-called BCOV homolorphic anomaly equation. This is a continuation of my previous talk in a similar workshop at TMU, Jan. 2012, but I will start with a brief summary of the backgrounds.

16:30-17:30 Martin Guest (Waseda University) "On the Riemann-Hilbert problem for the tt*-Toda equations"

Abstract: In an earlier article with Alexander Its and Chang-Shou Lin we computed the Stokes data (but not the connection matrix) for the "globally smooth" solutions of the tt*-Toda equation whose existence had been established by p.d.e. methods. We shall give an alternative proof of the existence of some of these solutions by solving a Riemann-Hilbert problem. In the process, we compute the connection matrix for all solutions, thus completing the computation of the monodromy data. We also give connection formulae relating the asymptotics of these solutions at zero and infinity.

Saturday 23 November

10:00-11:00 Masa-Hiko Saito (Kobe University) "Lagrangian fibrations in duality on moduli spaces of rank 2 logarithmic connections over the projective line"

Abstract: This talk is based on a joint work with Frank Loray. We consider the moduli space of the rank 2 logarithmic connections over ${\bf P}^1$ with $n$ singular points. There are two natural Lagrangian fibrations maps:one toward the apparent singularities and another one toward the moduli space of parabolic bundles. We will explain the structures of these fibrations. Moreover we will give a detailed description in the case of $n=4$ and $5$.

11:15-12:15 Daisuke Yamakawa (Tokyo Institute of Technology) "Fourier-Laplace transform and isomonodromic deformations"

Abstract: The Fourier-Laplace transform is an important tool for the study of meromorphic connections on the Riemann sphere. For instance, it is used to characterize the meromorphic connections "free of accessory parameters", and to construct Weyl group symmetries of some moduli spaces of meromorphic connections. In this talk, I will show that it induces a transformation of isomonodromic deformations under some reasonable assumptions, generalizing similar results of Harnad and Woodhouse.

LUNCH

14:00-15:00 Kazunori Miyazaki (Kobe University) "On compactifications of moduli of unramified irregular singular connections and Okamoto-Painleve pairs"

Abstract: There are ten types of rank two connections on the projective line whose (generalized) isomonodromic deformations induce Painleve equations. For the regular singular case, Inaba-Iwasaki-Saito constructed an isomorphism between the compactified moduli of connections and the Okamoto-Painleve pair of the Painleve VI equation. The next simplest four cases are unramified irregular singular connections. In this talk we will give the isomorphism for the unramified irrgular singular case.

15:30-16:30 Makoto Miura (Tokyo University) "Hibi toric varieties and mirror symmetry"

Abstract: I will talk on the mirror symmetry for some kinds of varieties which degenerate to complete intersections in Gorenstein Hibi toric varieties. A typical class of examples are Calabi-Yau complete intersections in minuscule Schubert varieties.


Previous workshops in this series;:

27 January 2012 Isomonodromic deformations and related topics

24 August 2010 Workshop on mirror symmetry and differential equations

17 August 2010 Workshop on tt*-geometry

23-26 June 2008 Workshop on pluriharmonic maps, meromorphic connections and quantum cohomology