Kobe Workshop on Quantum cohomology and Integrable systems
September 1 (Thu)--3 (Sat), 2011
Room B-314, Department of Mathemarics, Graduate School of Science, Kobe University
September 1, (Thursday)
	14:00--15:30
	M.-H. Saito (Kobe University)
	Geometry of moduli spaces of singular connections on curves
		In this talk, I would like to report on some joint works with M. Inaba, F. Loray, C. Simpson and S. Szabo. Since Inaba will give a talk on constructions the moduli spaces of stable parabolic connections with fixed formal type of regular or irregular singularities, I will give a brief introduction on it. Then I will discuss on an intrinsic way to give an apparent singularities of connections, which give a classical canonical coordinates (a joint work with S. Szabo). Then we will show that there are two Lagrangian fibrations on the moduli spaces of connections induced by apparent singularities map and also natural map to moduli spaces of parabolic bundles, which was reported in a joint work with F. Loray and C. Simpson.
	15:40--17:10
	M. Inaba (Kyoto University)
	Moduli of parabolic connections on a smooth projective curve
		In this talk, I will define the moduli space of stable parabolic connections with regular singularities on a smooth projective curve. There is Riemann-Hilbert morphism between the moduli space of parabolic connections and the moduli spave of the representations of the fundamental group. The main result is that Riemann-Hilbert morphism is a proper surjective bimeromorphic morphism. I will also talk about the moduli space of irregular singular parabolic connections on a smooth projecitve curve.
September 2, (Friday)
	10:00--11:30
	H. Iritani (Kyoto University)
	Fock sheaf associated to the semi-infinite Hodge
		Using Givental's quantization, we construct a Fock sheaf associated to a miniversal semi-infinite variation of Hodge structure. If time permits, I will also discuss the holomorphic anomaly equation.
	13:30--15:00
	C. Sabbah (E'cole polytechnique)
	Non-commutative Hodge structures
		The talk will give a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.
	15:30--17:00
	C.-L. Wang (National Taiwan University)
	Extension of quantum D modules and its application to analytic continuations
		In the study of analytic continuations of quantum cohomology rings under ordinary flops, the problem can be reduced to the local models which are certain toric bundles over an arbitrary base. The main purpose of this talk is to construct the Dubrovin connection of the bundle space as an extension of the base Dubrovin connection via the fiber Picard-Fuchs (GKZ) system. As an application we deduce the analytic continuation property. This is a joint project with Yuan-Pin Lee and Hui-Wen Lin.
September 3, (Saturday)
	10:00--11:30
	Y. Toda (IPMU)
	Multiple cover formula of generalized DT invariants
		The generalized DT invariants counting one dimensional semistable sheaves on Calabi-Yau 3-folds are conjectured to satisfy a certain multiple cover formula. In this talk, I explain an approach toward the multiple cover conjecture using Jacobian localizations and the notion of parabolic stable pairs.
	13:30--15:00
	C. Doran (University of Alberta)
	K3 Modular Parametrization and Calabi-Yau Threefold Variations
		We'll begin by recalling the Doran-Morgan classification of "mirror-compatible" integral variations of Hodge structure over the thrice punctured sphere. These fall into fourteen equivalence classes, according to shared real structures. Thirteen of these readily admit geometric realization via the Batyrev-Borisov mirror construction. The "14th case" has long proved elusive, despite strong hints coming from analysis of GKZ-hypergeometric systems and Hodge theory. A geometric solution will be presented, blending K3 surface fibrations, modular parametrizations, and a detailed analysis of (singular) toric hypersurfaces and complete intersections.
	15:30--17:00
	S. Hosono (University of Tokyo)
	BPS numbers of some Calabi-Yau threefolds
		In a recent collaboration with Hiromichi Takagi, we have found a new Calabi-Yau threefold as the double covering of a determinantal quintic ramified over a curve. This manifold fit into the classical projective geometry of Reye congruences. In this talk, I will focus on the BPS numbers of related Calabi-Yau threefolds with a brief summary about the structure of the BCOV holomorphic anomaly equations.
Organizers : Masa-Hiko Saito, Shinobu Hosono
Supported by JSPS Grant-in-Aid for Scientific Research (S)19104002 (PI: Masa-Hiko Saito)