Mini-workshop on Moduli of Instantons

Mini-workshop on Moduli of Instantons

Mar. 29 - Mar. 31, 2011

@ Nagoya university (Room 328 in Bldg. Sci. A)

The program has changed (March 26, 2011, 19:00 Japan Time).

Speakers

Bumsig Kim (KIAS)
Hiroaki Kanno (Nagoya)
Masato Taki (YITP, Kyoto)
Hiraku Nakajima (RIMS, Kyoto)
Kentaro Nagao (Nagoya)

Program

29th	10:30--11:30	Kim	Quasimaps and I-functions I
	13:00--14:30	Nagao changed !	Refined topological vertex via motivic Donaldson-Thomas invariants
	15:00--16:00	Kanno	Instanton counting with a surface operator and open topological string amplitudes I
	16:30--17:30	Taki	Surface operators, AGT relation and bubbling Calabi-Yau I
30th	10:30--11:30	Kim	Quasimaps and I-functions II
	13:00--14:30	Nakajima changed !	Quantum cohomology of the Springer resolution by Braverman-Maulik-Okounkov
	15:00--16:00	Kanno	Instanton counting with a surface operator and open topological string amplitudes II
	16:30--17:30	Taki	Surface operators, AGT relation and bubbling Calabi-Yau II
31th	10:30--11:30	Kim	Quasimaps and I-functions III
31th	13:00--14:30	TBA	TBA

Abstracts

Kim
- 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.
Kanno
- 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 [hep-th].
Taki
- Surface operators, AGT relation and bubbling Calabi-Yau I - II
  
  AGT relation is a mysterious duality between instanton counting in 4D gauge theories 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 Gopakumar-Vafa duality. I would also like to discuss the relation to the Hitchin system and other related topics.
Nagao
- Refined topological vertex via motivic Donaldson-Thomas invariants
  
  We provide a “motivic” 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.
(This workshop is supported by Grant-in-Aid for Research Activity Start-up 22840023)
AG seminar in Nagoya
Kentaro Nagao