Mini-workshop on Moduli of Instantons
Mar. 29 - Mar. 31, 2011
@ Nagoya university
(Room 328 in Bldg. Sci. A)
- Bumsig Kim  (KIAS)
- Hiroaki Kanno  (Nagoya)
- Masato Taki  (YITP, Kyoto)
- Hiraku Nakajima  (RIMS, Kyoto)
- Kentaro Nagao  (Nagoya)
|| Quasimaps and I-functions I
|| Nagao changed !
|| Refined topological vertex via motivic Donaldson-Thomas invariants
|| Instanton counting with a surface operator and open topological string amplitudes I
|| Surface operators, AGT relation and bubbling Calabi-Yau I
|| Quasimaps and I-functions II
|| Nakajima changed !
|| Quantum cohomology of the Springer resolution by Braverman-Maulik-Okounkov
|| Instanton counting with a surface operator and open topological string amplitudes II
|| Surface operators, AGT relation and bubbling Calabi-Yau II
|| Quasimaps and I-functions III
Quasimaps and I-functions I - III
In the lectures, I will construct the moduli space of stable quasimaps to a smooth GIT quotient W//G of an affine
variety W. The moduli space is virtually smooth when W is LCI and hence gives rise to
Gromov-Witten type theory (QGW) which is conjecturally equivalent to Gromov-Witten theory.
The comparison of both invariants, in particular, the I-function and the J-function, will be discussed.
I will also explain how to get a new class of examples with symmetric obstruction theory
by applying this quasimap construction to Nakajima quiver varieties W//G.
Instanton counting with a surface operator and open topological string amplitudes I - II
We test the agreement of the instanton partition function
in the presence of the surface operator with open topological
string amplitudes, which is regarded as a geometric engineering
of the surface operator proposed by S. Gukov. The instanton
partition function in the presence of the surface operator is
computed by the localization on the moduli space of parabolic
torsion free sheaves. This talk is based on a collaboration with
H.~Awata, H.~Fuji, M.~Manabe and Y.~Yamada, arXiv:1008.0574
Surface operators, AGT relation and bubbling Calabi-Yau I - II
AGT relation is a mysterious duality between instanton counting in 4D
and the representation theory of the W algebras.
In this talk I study string theoretical aspects of the duality
in the presence of surface operators of 4D gauge theories, which is a
ramified version of AGT relation.
After reviewing these topics,
we find a deep connection between the ramified version of AGT and the
I would also like to discuss the relation to the Hitchin system and
other related topics.
- Refined topological vertex via motivic Donaldson-Thomas invariants
We provide a gmotivich version of the result of [Nagao-Nakajima].
An explicit formula of the generating function of the motivic Donaldson-Thomas invariants is given for any chamber.
As a consequence, we realize the refined topological vertex as the generating function of the motivic Donaldson-Thomas invariants.