Yukiko Konishi

FLOP INVARIANCE OF THE TOPOLOGICAL VERTEX

We prove transformation formulae for generating functions of Gromov–Witten invariants on general toric Calabi–Yau threefolds under flops. Our proof is based on a combinatorial identity on the topological vertex and analysis of fans of toric Calabi–Yau threefolds.

Asymptotic form of Gopakumar-Vafa invariants from instanton counting

We study the asymptotic form of the Gopakumar–Vafa invariants at all genera for Calabi–Yau toric threefolds which have the structure of fibration of the An singularity over P 1 . We claim that the asymptotic form is the inverse Laplace transform of the corresponding instanton amplitude in the prepotential of N = 2 SU(n + 1) gauge theory coupled to external graviphoton fields, which is given by the logarithm of the Nekrasov’s partition function.  2004 Elsevier B.V. All rights reserved.

Geometric engineering of Seiberg-Witten theories with massive hypermultiplets

Abstract We analyze the geometric engineering of the N=2 SU(2) gauge theories with 1⩽Nf⩽3 massive hypermultiplets in the vector representation. The set of partial differential equations satisfied by the periods of the Seiberg–Witten differential is obtained from the Picard–Fuchs equations of the local B-model. The differential equations and its solutions are consistent with the massless case. We show that the Yukawa coupling of the local A-model gives rise to the correct instanton expansion in the gauge theory, and propose the pattern of the distribution of the world-sheet instanton number from it. As a side result, we obtain the asymptotic form of the instanton amplitude in the gauge theories with massless hypermultiplets.

Multi-Hamiltonian Structures on Beauville's Integrable System and Its Variant ?

We study Beauvilles completely integrable system and its variant from a view- point of multi-Hamiltonian structures. We also relate our result to the previously known Poisson structures on the Mumford system and the even Mumford system.