KGPD 2014 (Koriyama Geometry and Physics Days 2014)
Second meeting: String topology, orbifolds, and related topics,
October 4(Sat) 14:00 --6(Mon) 13:00, 2014
5F, Building 55, College of Engineering, Nihon University (Koriyama, Fukushima),
Access to the campus,
Bus time table from/to Koriyama station to/from the campus
Caution: The main gate will be closed on Oct 4 and 5. This should be useful:
From the bus stop to the Building 55
Katsuhiko Kuribayashi (Shinshu), Kenji Mohri (Tsukuba), Hironori Sakai (Münster)
Takahito Naito (Tokyo), Hiraku Abe (Osaka City University Advanced Mathematical Institute)
, Takashi Otofuji (Nihon University)
Main literature of KGPD 2014:
A. Gonzalez, E. Lupercio, C. Segovia and B. Uribe:   Orbifold Topological Quantum Field Theories in Dimension 2
SAT (4 Oct)
14:00-14:30 Otofuji: Overview
14:40-15:40 Mohri: Open-Closed Topological Field Theory in Two Dimensions (after Moore and Segal), 1st lecture
15:40-16:00 Coffee break
16:00-17:30 Abe: Orbifolds
SUN (5 Oct)
9:30-10:00 Discussion with tea
10:00-11:00 Sakai: The symplectic vortex equations and Gromov-Witten invariants, 1st lecture
11:10-12:10 Kuribayashi: Derived string topology, 1st lecture
14:00-15:00 Naito: String topology operations on rational Gorenstein spaces
15:00-15:20 Coffee break
15:20-16:20 Mohri Open-Closed Topological Field Theory in Two Dimensions (after Moore and Segal), 2nd lecture
16:30-17:30 Otofuji: From dGBV algebras to Frobenius manifolds (after Barannikov-Kontsevich)
MON (6 Oct)
9:30-10:00 Discussion with tea
10:00-11:30 Kuribayashi: Derived string topology, 2nd lecture
11:40-12:40 Sakai:The symplectic vortex equations and Gromov-Witten invariants, 2nd lecture
Titles and abstracts:
Hiraku Abe (Osaka City University Advanced Mathematical Institute)
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.
[F-T] Y. Félix and J. -C. Thomas, String topology on Gorenstein spaces,
Math. Ann. 345 (2009), no. 2, 417-452.
[K-L-N1] K. Kuribayashi, L. Menichi and T. Naito, Behavior of the Eilenberg-Moore spectral sequence
in derived string topology, Topology and its Applications, 164 (2014), 24-44.
[K-L-N2] K. Kuribayashi, L. Menichi and T. Naito, Derived string topology and
the Eilenberg-Moore spectral sequence, to appear in Israel Journal of Mathematics, arXiv: math.AT/1211.6833
Kenji Mohri (Tsukuba)
Open-Closed Topological Field Theory in Two Dimensions (after Moore and Segal) (2 lectures)
Takahito Naito (Tokyo)
String topology operations on rational Gorenstein spaces
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.
KGPD 2014 First meeting
KGPD 2014 Literature
This conference is supported by JSPS Grant-in-Aid for Scientific Research (A) 25247005 (PI: