
The 1982 paper of Atiyah and Bott on "The YangMills equations over Riemann surfaces" started a vigorous period of research into the symplectic and Poisson geometry of moduli spaces of flat connections on vector bundles over surfaces. By generalizing to bundles with complex structural groups, Hitchin introduced Higgs bundles, which have deep connections to the theory of integrable systems. Donaldson, JeffreyWeitsmann and AlekseevMalkinMeinrenkenWoodward studied bundles over surfaces with boundary (or connections with regular singularities), revealing new connections with Poisson geometry. Boalch developed the theory for connections with irregular singularities, which arise naturally in the theory of Painleve equations and also in the theory of Frobenius manifolds. At the same time, the early relations with differential geometry and variations of Hodge structures remain important. The talks in this workshop will address several of these topics.
NishiWaseda Campus access map
Photographs from the workshop: Group 1 Group 2
Speakers:
ChiKwong Fok (National TsingHua University)
TITLE: Twisted Poisson manifolds and their almost symplectically complete isotropic
realizations
ABSTRACT: Let B be a twisted Poisson manifold with a fixed tropical affine
structure. In this talk, we will discuss the classification of almost symplectically
complete isotropic realizations (ASCIRs) over B in the spirit of DazordDelzant.
We will construct a product among ASCIRs in analogy with tensor product of line
bundles, thereby introducing the notion of the Picard group of B. We will give
descriptions of the Picard group and the corresponding 'NeronSeveri group'
using certain sheaf cohomology groups. This is joint work with Reyer Sjamaar.
Martin Guest (Waseda University)
TITLE: Moduli spaces of real solutions of the third Painleve equation (joint work with Claus Hertling)
NanKuo Ho (National TsingHua University)
TITLE: Hitchin's equations over a nonorientable manifoldKohei Iwaki (RIMS, Kyoto University)
TITLE: Part 1: Introduction to exact WKB analysis, Part 2: Exact WKB analysis
and cluster algebras
ABSTRACT: Exact WKB analysis is an effective method for the global study of
differential equations (containing a large parameter) defined on a complex domain.
On the other hand, a cluster algebras is a particular class of commutative subalgebra
of a field of rational functions with distinguished generators. In this talk
I'll explain about a hidden cluster algebraic structure in exact WKB analysis.
I'll give an introduction to the theory of exact WKB analysis in the first talk.
The second talk will be devoted to an explanation of our main results. My talk
is based on a joint work with T. Nakanishi (Nagoya).
MasaHiko Saito (Kobe University)
TITLE: Canonical coordinates of moduli spaces of parabolic connections and
parabolic Higgs bundles (joint work with Szilard Szabo)
ABSTRACT: In the first part of the talk, we will review on the algebraic construction
of the moduli spaces of parabolic connections and parabolic Higgs bundles on
curves. Then we review new results on canonical coordinates of their moduli
spaces by so called apparent singularities.
Yoshihiro Ohnita (Osaka City University and OCAMI)
TITLE: Gaugetheoretic approach to harmonic maps and subspaces in moduli spaces (joint work with Mariko MukaiHidano)
Eugene Xia (National ChengKung University)
TITLE: Higgs bundle and representation variety
ABSTRACT: This presentation
introduces the subject of nonabelian cohomology, more specifically, the correspondences
of the representation varieties, the moduli spaces of smooth, holomorphic and
algebraic flat connections and the moduli spaces of Higgs bundles on a smooth
projective variety. Striking geometric and topological results are obtained
through these correspondences.
Daisuke Yamakawa (Tokyo Institute of Technology)
TITLE: Isomonodromic deformations from Hamiltonian point of view
SCHEDULE OF TALKS:
Saturday 15 November 2014 10:00
10:1511:15 Ohnita
11:3012:30 Xia
lunch break
14:0015:00 Ho
15:1516:15 Iwaki (1)
coffee/tea break
16:4517:45 Saito
Sunday 16 November 2014 10:00
10:1511:15 Fok
11:3012:30 Guest
lunch break
14:0015:00 Iwaki (2)
15:1516:15 Yamakawa
Organizing committee: Martin Guest (Waseda University), NanKuo Ho (National TsingHua University, Taiwan), Yoshihiro Ohnita (Osaka City University)
Sponsors:
JSPS GrantinAid for Scientific Research (A)25247005 (PI: Martin Guest) "Systematic development and application of methods in differential geometry and integrable systems motivated by quantum cohomology"
JSPS GrantinAid for Scientific Research (S)24224001 (PI: MasaHiko Saito)
"Developments in Interactions between Algebraic Geometry and Integrable
Systems"
JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers (Oct. 2014Mar. 2017) "Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI" (Osaka City University  Kobe University  Waseda University, PI: Yoshihiro Ohnita)