We will take a quick overview of orbifolds (in terms of Lie groupoids) and the stringy cohomology rings for global quotient orbifolds.


Katsuhiko Kuribayashi (Shinshu) : Derived string topology   (2 lectures)

We begin with an introduction of string topology initiated by Chas and Sullivan. Roughly speaking, the study of string topology is to consider fruitful structures on the homology of the free loop spaces, the so-called loop homology, of manifolds and more general spaces. The loop (co)products are prime and important string operations on the loop homology. We describe these products in terms of the torsion functors with advantages of derived string topology on Gorenstein spaces due to Félix and Thomas. The class of Gorenstein spaces contains closed orientable manifolds and the classifying spaces of Lie groups. Thus our description is applicable to the setting of the original loop (co)products and to string topology of classifying spaces due to Chataur and Menichi. Moreover, such algebraic interpretation of the products permits us to construct the Eilenberg-Moore spectral sequence (EMSS) for the loop homology. In the end of the talk, computational examples of the loop homology with the EMSS are given.

The theory of string topology is developed to Gorenstein spaces by Felix and Thomas. In this talk, we introduce about string topology on rational Gorenstein spaces. Moreover, we give some computational examples of string topology operations.


Takashi Otofuji (Nihon University) : From dGBV algebras to Frobenius manifolds (after Barannikov-Kontsevich)

We review the construction of Frobenius manifolds from differential Gerstenhaber-Batalin-Vilkovisky algebras due to Barannikov-Kontsevich.


Hironori Sakai (Münster): The symplectic vortex equations and Gromov-Witten invariants   (2 lectures)

The symplectic vortex equations (SVE for short) are PDEs associated to a symplectic manifold equipped with a Hamiltonian action. If the Hamiltonian action is a (standard) representation of a closed subgroup of a unitary group, the theory of SVEs gives a gauged sigma-model.

One of the important fact of the theory is: Making use of the moduli space of the solutions of SVE, we can define invariants of Hamiltonian actions. Under certain assumptions, the invariants agree with Gromov-Witten invariants of the symplectic quotient.
In these talks we study basic facts about SVEs and recent development in relation to geometry of orbifolds.

TMUGS