Workshops

Flat connections, Higgs bundles and Painleve equations

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May 1 - 5, 2016 
101, Mathematics Research Center Building (ori. New Math. Bldg.)


In recent years there has been much progress concerning the geometry of moduli spaces of flat connections, Higgs bundles, and their relation to integrable systems such as Hitchin systems and Painleve equations. For example, isomonodromic deformations of singular flat connections on Riemann surfaces induce nonlinear differential equations of Painleve type including classical Painleve equations. The family of moduli spaces of singular connections gives the phase space of such a differential equation. This is related to the fact that the phase spaces of Hitchin integrable systems are given by moduli spaces of Higgs bundles.

The main purpose of this workshop is to discuss recent progress related to the geometry of moduli space of flat connections, Higgs bundles, and their relations with integrable systems. Every invited speaker will give two fifty minute lectures.

Invited SpeakersPhilip Boalch ( Université Paris-Sud, France )
Martin A. Guest ( Waseda University, Japan )
Claus Hertling ( University of Mannheim, Germany )
Alexander R. Its ( Indiana University-Purdue University Indianapolis, USA )
Yuan-Pin Lee ( University of Utah, USA & National Taiwan University )
Chang-Shou Lin ( National Taiwan University )
Takuro Mochizuki ( Kyoto University, Japan )
Claude Sabbah ( École Polytechnique, France )
Masa-Hiko Saito ( Kobe University, Japan )
Chin-Lung Wang ( National Taiwan University )
OrganizersMartin A. Guest ( Waseda University, Japan )
Chang-Shou Lin ( Department of Mathematics, National Taiwan University )
Masa-Hiko Saito ( Kobe University, Japan )
SponsorsTaida Institute for Mathematical Sciences ( TIMS )
Waseda University, Japan
Osaka City University Advanced Mathematical Institute, Japan  (OCAMI)
JSPS Grant-in-Aid for Scientific Research (S)24224001 (PI: M.-H. Saito), Japan
RegistrationRegistraion page is closed, please contact TIMS for participation information.
More InformationFor any further information, please consult the above menu links or contact TIMS.
Program
May. 1 (Sun.) 
12:30 ~ 12:50Registration
12:50 ~ 13:00Open Session
13:00 ~ 13:50Takuro Mochizuki Asymptotic behaviour of certain families of harmonic bundles on Riemann surface
14:00 ~ 14:50Takuro Mochizuki Asymptotic behaviour of certain families of harmonic bundles on Riemann surface
14:50 ~ 15:20Coffee Break
15:20 ~ 16:10Chin-Lung Wang Dubrovin connection under flips
16:20 ~ 17:10Chin-Lung Wang Dubrovin connection under flips
May. 2 (Mon.)
10:00 ~ 10:50Philip Boalch Non-perturbative symplectic manifolds and non-commutative algebras
11:00 ~ 11:50Philip Boalch Hyperkahler manifolds from connections and quivers
12:00 ~ 13:30Lunch
13:30 ~ 14:20Masa-Hiko Saito An explicit geometry of moduli spaces of Higgs bundles and Singular connections on a smooth curve and differential equations of Painlevé types
14:30 ~ 15:20Masa-Hiko Saito An explicit geometry of moduli spaces of Higgs bundles and Singular connections on a smooth curve and differential equations of Painlevé types
15:20 ~ 15:50Coffee Break
15:50 ~ 16:40Claus Hertling The Painlevé III equation of type (0,0,4,-4), associated vector bundles with additional structure, and the geometry of the movable poles of real solutions
16:50 ~ 17:40Claus Hertling The Painlevé III equation of type (0,0,4,-4), associated vector bundles with additional structure, and the geometry of the movable poles of real solutions
18:30 ~Banquet
May. 3 (Tue.)
10:00 ~ 10:50Yuan-Pin Lee 
10:00 ~ 10:50Yuan-Pin Lee Gromov-Witten theory and variation of Hodge structure under conifold transitions for Calabi-Yau threefolds
12:00 ~ 13:30Lunch
13:30 ~ 18:00Free Time
May. 4 (Wed.)
10:00 ~ 10:50Alexander R. Its Monodromy dependence and connection formulae for isomonodromic tau functions
11:00 ~ 11:50Alexander R. Its Monodromy dependence and connection formulae for isomonodromic tau functions
12:00 ~ 13:30Lunch
13:30 ~ 14:20Claude Sabbah Exponential Hodge theory (I)
14:30 ~ 15:20Claude Sabbah Exponential Hodge theory (II)
15:20 ~ 15:50Coffee Break
15:50 ~ 16:40Chang-Shou Lin Some applications of Painlevé VI
16:50 ~ 17:40Chang-Shou Lin Some applications of Painlevé VI
May. 5 (Thu.)
10:00 ~ 10:50Martin A. Guest Harmonic maps of Painlevé-type: the loop group point of view
11:00 ~ 11:50Martin A. Guest Harmonic maps of Painlevé-type: the loop group point of view
12:00 ~ 13:30Lunch
Flat connections, Higgs bundles and Painleve equations