Quasimap Theory WI24

Time and location: Mondays 2-3:30pm, Linde 387

Organizer: Song Yu

The goal of this learning seminar is to survey the theory of quasimaps and its applications. Here is a tentative list of topics:

The basic theory and constructions of quasimaps
Wall-crossings and mirror symmetry
Connections to other enumerative theories

Here is a list of references:

[BCK] A. Bertram, I. Ciocan-Fontanine, B. Kim, Gromov-Witten invariants for abelian and nonabelian quotients
[CCK] D. Cheong, I. Ciocan-Fontanine, B. Kim, Orbifold quasimap theory
[CIR] A. Chiodo, H. Iritani, Y. Ruan, Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence
[CR] A. Chiodo, Y. Ruan, Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations
[CK1] I. Ciocan-Fontanine, B. Kim, Moduli stacks of stable toric quasimaps
[CK2] I. Ciocan-Fontanine, B. Kim, Wall-crossing in genus zero quasimap theory and mirror maps
[CK3] I. Ciocan-Fontanine, B. Kim, Higher genus quasimap wall-crossing for semi-positive targets
[CK4] I. Ciocan-Fontanine, B. Kim, Big I-functions
[CK5] I. Ciocan-Fontanine, B. Kim, Quasimap theory
[CK6] I. Ciocan-Fontanine, B. Kim, Quasimap wall-crossings and mirror symmetry
[CKM] I. Ciocan-Fontanine, B. Kim, D. Maulik, Stable quasimaps to GIT quotients
[CKS] I. Ciocan-Fontanine, B. Kim, C. Sabbah, The abelian/nonabelian correspondence and Frobenius manifolds
[CJR] E. Clader, F. Janda, Y. Ruan, Higher-genus quasimap wall-crossing via localization
[CLS] T. Coates, W. Lutz, Q. Shafi, The abelian/non-abelian correspondence and Gromov-Witten invariants of blow-ups
[GR] S. Guo, D. Ross, Genus-one mirror symmetry in the Landau–Ginzburg model
[KL] B. Kim, H. Lho, Mirror theorem for elliptic quasimap invariants
[MOP] A. Marian, D. Oprea, R. Pandharipande, The moduli space of stable quotients
[RR] D. Ross, Y. Ruan, Wall-crossing in genus zero Landau-Ginzburg theory
[W] R. Webb, Abelian-nonabelian correspondence for I-functions
[Z] Y. Zhou, Quasimap wall-crossing for GIT quotients

Here is a tentative schedule:

Date	Topics	References
1/8	Introduction - quasimaps to toric varieties	[CK5, CK1]
1/15	Quasimaps to GIT quotients	[CKM]
1/22	Genus-zero wall-crossing and mirror symmetry	[CK2]
*1/29	No meeting - Miami conference
2/5	Genus-zero wall-crossing cont'd, I-functions	[CK2, CK4, CCK]
2/12	Higher-genus wall-crossing for semi-positive targets	[CK3]
*2/19	No meeting - President's Day
2/26	(by Thorgal Hinault) Wall-crossing for general targets	[Z]
3/4	Quasimaps and LG/CY correspondence	[CR, CIR, RR]
3/11	Abelian/nonabelian correspondence	[BCK, CKS, W, CLS]

Quasimap Theory Winter 2024