Publications by subjects

Gromov-Witten theory and related fields:

Survey papers

Notes on orbifold Gromov-Witten theory, in Fifth International Congress of Chinese Mathematicians Part 1, AMS/IP Studies in Advanced Mathematics, vol. 51, Amer. Math. Soc., Providence, RI, 2012, pp. 327--340.

Mirror theorem, Seidel representation, and counting holomorphic disks in toric varieties, in Proceedings of the Sixth International Congress of Chinese Mathematicians Vol. I, 489--503, Advanced Lectures in Mathematics (ALM), 36, Int. Press, Somerville, MA, 2017.

A survey on toric mirror symmetry, in: "Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations", 453--473, Adv. Lect. Math. (ALM), 42, Int. Press, Somerville, MA, 2018.

On the geometry of orbifold Gromov-Witten invariants, arXiv:1703.08918, in Proceedings of the Seventh International Congress of Chinese Mathematicians Vol. I, 439--456, Advanced Lectures in Mathematics (ALM), 43, Int. Press, Somerville, MA, 2019.

Papers on structural results

(with Dan Abramovich, Tom Graber, and Martin Olsson) On The Global Quotient Structure of The Space of Twisted Stable Maps to a Quotient Stack, arXiv:math.AG/0502253, Journal of Algebraic Geometry 16 (2007),731--751 link.

Orbifold Quantum Riemann-Roch, Lefschetz and Serre, arXiv:math.AG/0506111, Geometry and Topology 14 (2010) 1--81 link.

(with Elena Andreini and Yunfeng Jiang) Gromov-Witten theory of product stacks, arXiv:0905.2258, Communications in Analysis and Geometry 24 (2016), no. 2, 223--277 link.

(with Deniz Genlik) Holomorphic anomaly equations for C^5/Z_5, arXiv:2211.15878, to appear in Bumsig Kim memorial volume.

(with Shidhesh Supekar) Wall-crossing for quasimaps to GIT stack bundles, arXiv:2212.00910, Journal of London Mathematical Society (2) 111 (2025), no. 6, Paper No. e70185, 50 pp link.

(with Deniz Genlik) Higher Genus Gromov-Witten Theory of C^n/Z_n I: Holomorphic Anomaly Equations, arXiv:2301.08389, Advances in Mathematics 444, Article ID 109634, 75 p. (2024) link.

(with Yunfeng Jiang) On counting plurifibered varieties, arXiv:2306.08747, preprint.

Papers on calculations

(with Tom Coates, Alessio Corti, and Yuan-Pin Lee) The Quantum Orbifold Cohomology of Weighted Projective Space, arXiv:math.AG/0608481, Acta Mathematica, Volume 202, Number 2 (2009), 139--193 link.

(with Tom Coates, Alessio Corti, and Hiroshi Iritani) Computing Genus-Zero Twisted Gromov-Witten Invariants, arXiv:math.AG/0702234, Duke Mathematical Journal, Volume 147, Number 3 (2009), 377--438 link.

(with Paul Johnson and Rahul Pandharipande) Abelian Hurwitz-Hodge integrals, arXiv:0803.0499, Michigan Mathematics Journal 60 (2011), Issue 1, 171--198 link.

(with Paul Johnson and Rahul Pandharipande) Notes on local P^1-orbifolds, preprint, link.

On degree zero elliptic orbifold Gromov-Witten invariants, arXiv:0912.3580, International Mathematics Research Notices Vol. 2011, no. 11, 2444--2468 link.

(with Amin Gholampour) On computations of genus zero two-point descendant Gromov-Witten invariants, arXiv:1207.6071, Michigan Mathematics Journal 62 (2013), no. 4, 753--768 link.

(with Yunfeng Jiang and Fenglong You) The Quantum Orbifold Cohomology of Toric Stack Bundles, arXiv:1503.00155, Letters in Mathematical Physics 107 (2017), no. 3, 439--465 link.

(with Yunfeng Jiang) Hypertoric geometry and Gromov-Witten theory, arXiv:1506.02065, Journal of Geometry and Physics 126 (2018), 101--126 link.

(with Sagnik Das and Yunfeng Jiang) The quantum cohomology of moduli space of $PGL_2$-bundles on curves, arXiv:2405.06562, submitted.

Crepant resolution correspondence

(with Tom Coates and Hiroshi Iritani) Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples, arXiv:math.AG/0611550, Geometry and Topology 13 (2009) 2675--2744 link.

(with Tom Coates, Alessio Corti, and Hiroshi Iritani) The Crepant Resolution Conjecture for Type A Surface Singularities, arXiv:0704.2034, appeared as appendix of arXiv:math.AG/0702234.

(with Yunfeng Jiang) The Crepant Transformation Conjecture implies the Monodromy Conjecture, arXiv:1507.00254, Mathematical Research Letters Volume 26 (2019), no. 5, 1437--1465 link.

(with Deniz Genlik) On Hilb/Sym correspondence for K3 surfaces, arXiv:2304.06536, to appear in Canadian Mathematical Bulletin.

(with Deniz Genlik) Higher Genus Gromov-Witten Theory of C^n/Z_n II: Crepant Resolution Correspondence, arXiv:2308.00780, submitted.

(with Qian Chao and Jiun-Cheng Chen) Crepant Transformation Correspondence For Toric Stack Bundles, arXiv:2410.22670, to appear in Advances in Geometry.

Seidel representations

Seidel representation for Symplectic orbifolds, revised version of preprint 2004, superseded by arXiv:1207.4246 below.

(with Dongning Wang) Seidel Representation for Symplectic Orbifolds, arXiv:1207.4246, preprint.

(with Dongning Wang) Seidel Representations and Quantum Cohomology of Toric Orbifolds, arXiv:1211.3204, preprint.

Gromov-Witten theory of Hilbert schemes of points in the affine plane

(with Rahul Pandharipande) Higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and CohFTs associated to local curves, arXiv:1707.01406, Forum of Mathematics Pi, Volume 7 (2019), e4 link.

(with Rahul Pandharipande) The Hilb/Sym correspondence for C2: descendents and Fourier-Mukai, arXiv:1807.06969, Mathematische Annalen, Volume 375 (2019), Issue 1-2, pp 509--540 link.

(with Aitor Iribar Lopez and Rahul Pandharipande) Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Noether-Lefschetz theory of $\mathcal{A}_g$, arXiv:2506.12438, submitted.

A trilogy on Gromov-Witten theory of toric stacks

(with Tom Coates, Alessio Corti, and Hiroshi Iritani) A mirror theorem for toric stacks, arXiv:1310.4163, Compositio Mathematica 151 (2015), no. 10, 1878--1912 link.

(with Tom Coates, Alessio Corti, and Hiroshi Iritani) Some Applications of the Mirror Theorem for Toric Stacks, arXiv:1401.2611, Advances in Theoretical and Mathematical Physics Volume 23 (2019), no. 3, 767--802 link.

(with Tom Coates, Alessio Corti, and Hiroshi Iritani) Hodge-Theoretic Mirror Symmetry for Toric Stacks, arXiv:1606.07254, Journal of Differential Geometry 114 (2020), no. 1, 41--115 link.

Orbifold Gromov-Witten theory in codimension one

(with Fenglong You) On orbifold Gromov-Witten theory in codimension one, arXiv:1509.02624, Journal of Pure and Applied Algebra 220 (2016), no. 10, 3567--3571 link.

(with Fenglong You and Zhengyu Zong) Double ramification cycles on the moduli spaces of admissible covers, arXiv:1606.03770, preprint.

(with Fenglong You) Higher genus relative and orbifold Gromov-Witten invariants of curves, arXiv:1804.09905, preprint.

(with Fenglong You) Higher genus relative and orbifold Gromov-Witten invariants, arXiv:1806.11082, Geometry and Topology 24 (2020) 2749--2779 link.

(with Honglu Fan and Fenglong You) Mirror theorems for root stacks and relative pairs, arXiv:1811.10807, Selecta Mathematica Volume 25, Article number: 54 (2019) link.

(with Fenglong You) On the polynomiality of orbifold Gromov--Witten theory of root stacks, arXiv:2001.00244, Mathematische Zeitschrift Volume 300, pages 235--246 (2022) link.

(with Fenglong You) A mirror theorem for multi-root stacks and applications, arXiv:2006.08991, Selecta Mathematica Volume 29, Article number: 6 (2023) link.

(with Fenglong You) A Gromov-Witten theory for simple normal-crossing pairs without log geometry, arXiv:2008.04844, Communications in Mathematical Physics 401, No. 1, 803--839 (2023) link.

(with Luca Battistella, Navid Nabijou, and Fenglong You) The local-orbifold correspondence for simple normal crossings pairs, arXiv:2103.09299, Journal of the Institute of Mathematics of Jussieu 22, No. 5, 2515--2531 (2023) link.

Gromov-Witten theory and integrable systems

(with Todor Milanov) The spaces of Laurent polynomials, P^1-orbifolds, and integrable hierarchies, arXiv:math.AG/0607012, Journal für die reine und angewandte Mathematik (Crelle's Journal), Volume 2008, Issue 622, Pages 189--235 link.

(with Yunfeng Jiang) On Virasoro Constraints for Orbifold Gromov-Witten Theory, arXiv:0704.2009, International Mathematics Research Notices, Vol. 2010, no. 4, 756--781 link.

(with Todor Milanov) Equivariant orbifold structures on the projective line and integrable hierarchies, arXiv:0707.3172, Advances in Mathematics 226 (2011), Issue 1, 641--672 link.

(with Yunfeng Jiang) Virasoro constraints and descendant Hurwitz-Hodge Integrals, arXiv:0804.3631, International Mathematics Research Notices Vol. 2010, no. 8, 1456--1474 link.

(with Todor Milanov and Yefeng Shen) Gromov-Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies, arXiv:1401.5778, Geometry and Topology 20 (2016) 2135--2218 link.

(with Tom Coates, and Alexander Givental) Virasoro constraints for toric bundles, arXiv:1508.06282, Forum of Mathematics Pi 12, Paper No. e4, 28 p. (2024) link.

A note on Virasoro constraints for products, submitted.

Gromov-Witten theory of gerbes

(with Elena Andreini and Yunfeng Jiang) On Gromov-Witten theory of root gerbes, arXiv:0812.4477, preprint.

(with Elena Andreini and Yunfeng Jiang) Gromov-Witten theory of root gerbes I: structure of genus $0$ moduli spaces, arXiv:0907.2087, Journal of Differential Geometry 99 (2015), no. 1, 1--45 link.

(with Elena Andreini and Yunfeng Jiang) Gromov-Witten theory of banded gerbes over schemes, arXiv:1101.5996, preprint.

(with Xiang Tang) A quantum Leray-Hirsch theorem for banded gerbes, arXiv:1602.03564, Journal of Differential Geometry Vol. 119, Issue 3 (Nov 2021), 459--511 link.

On Gromov-Witten Theory of Toric Gerbes, Albanian Journal of Mathematics volume 14 (2020), no. 1, 3--23 link.

(with Xiang Tang) On gerbe duality and relative Gromov-Witten theory, arXiv:1910.04272, Advances in Theoretical and Mathematical Physics Vol. 25 (2021), No. 8, 2171--2178 link.

K-theoretic Gromov-Witten type theories

(with Valentin Tonita) Quantum orbifold Hirzebruch-Riemann-Roch theorem in genus zero, arXiv:1307.0262, submitted.

(with Fenglong You) K-theoretic quasimap invariants and their wall-crossing, arXiv:1602.06494, preprint.

(with Fenglong You) Wall-Crossing in Genus Zero K-theoretic Landau-Ginzburg Theory, arXiv:1609.08176, preprint.

(with David Anderson and Linda Chen) On the quantum K-ring of the flag manifold, arXiv:1711.08414, preprint.

(with David Anderson and Linda Chen, with an appendix by Hiroshi Iritani) On the finiteness of quantum K-theory of a homogeneous space, arXiv:1804.04579, International Mathematics Research Notices, Vol. 2022, No. 2, pp. 1313--1349 link.

A note on quantum K-theory of root constructions, arXiv:2305.15655, Glasgow Mathematical Journal 66, No. 3, 494--500 (2024) link.

Donaldson-Thomas theory

(with Amin Gholampour) On Donaldson-Thomas invariants of threefold stacks and gerbes, arXiv:1001.0435, Proceedings of American Mathematical Society 141 (2013), no. 1, 191--203 link.

Open Gromov-Witten theory

Disks in toric manifolds
- (with Kwokwai Chan and Siu-Cheong Lau) Enumerative meaning of mirror maps for toric Calabi-Yau manifolds, arXiv:1110.4439, Advances in Mathematics 244 (2013) 605--625 link.
- (with Kwokwai Chan, Siu-Cheong Lau and Naichung Conan Leung) Open Gromov-Witten invariants and mirror maps for semi-Fano toric manifolds, arXiv:1112.0388, Pure and Applied Mathematics Quarterly Volume 16 (2020), no. 3, 675--720 link.
- (with Kwokwai Chan, Siu-Cheong Lau and Naichung Conan Leung) Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds, arXiv:1209.6119, Duke Mathematical Journal Volume 166, Number 8 (2017), 1405--1462 link.

Disks in toric orbifolds
- (with Kwokwai Chan, Cheol-Hyun Cho, and Siu-Cheong Lau) Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds, arXiv:1208.5282, Communications in Mathematical Physics 328 (2014), no. 1, 83--130 link.
- (with Bohan Fang and Chiu-Chu Melissa Liu) Open-closed Gromov-Witten invariants of $3$-dimensional Calabi-Yau smooth toric DM stacks, arXiv:1212.6073, Forum of Mathematics Sigma 10, e58 (2022) link.
- (with Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau) Gross fibraiton, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds, arXiv:1306.0437, Journal of Differential Geometry 103 (2016), no. 2, 207--288 link.
- (with Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau and Naichung Conan Leung) A note on disk counting in toric orbifolds, arXiv:1902.05904, SIGMA 16 (2020), 055, 15 pages link.

Tautological classes

On Orbifold Gromov-Witten Classes, arXiv:2112.15313, Portugaliae Mathematica 79 (2022), no. 3/4, pp. 395--403 link.

On the tautological rings of stacks of twisted curves, arXiv:2205.05529, Kyoto Journal of Mathematics 65, No. 4, 907--917 (2025) link.

Vafa-Witten theory

(with Yunfeng Jiang) A proof of all ranks S-duality conjecture for K3 surfaces, arXiv:2003.09562, Asian Journal of Mathematics 28, No. 2, 317-344 (2024) link.

(with Yunfeng Jiang) On multiple cover formula for local K3 gerbes, arXiv:2201.09315, Pure and Applied Mathematics Quarterly, 17 (2021), no. 5, 2005--2080 link.

Geometry of stacks/orbifolds:

Characteristic classes

Chern classes of Deligne-Mumford stacks and their coarse moduli spaces, arXiv:0709.0034, American Journal of Mathematics 133 (2011), no. 1, 29--38 link.

(with Jiun-Cheng Chen) On the Bogomolov-Miyaoka-Yau inequality for Deligne-Mumford surfaces, arXiv:1101.3481, Taiwanese Journal of Mathematics Volume 24 (2020) No. 4, 841--853 link.

(with Ajay Ramadoss and Xiang Tang) Hochschild Lefschetz Class for $D$-modules, arXiv:1203.6885, Mathematische Zeitschrift, Volume 275 (2013), Issue 1-2, 367--388 link.

(with Qiaochu Ma, Xiang Tang, and Zhaoting Wei) Superconnection and Orbifold Chern character, arXiv:2505.13912, submitted.

Gerbes

(with Xiang Tang) Duality theorems of étale gerbes on orbifolds, arXiv:1004.1376, Advances in Mathematics 250 (2014), 496--569 link.

(with Xiang Tang) Conjugacy classes and characters for extensions of finite groups, arXiv:1310.6384, Chinese Annals of Mathematics, Series B, Volume 35 (2014), Issue 5, pp 743--750 link.

(with Ilya Shapiro and Xiang Tang) On the relative dual of an S^1-gerbe over an orbifold, arXiv:1312.7316, Advances in Mathematics 270 (2015), 1--20 link.

Categories

(with Yu-Han Liu) Stacks associated to abelian tensor categories, arXiv:1206.0076, preprint.

Other topics:

Lie algebroids

(with Chenchang Zhu) Integrating Lie algebroids via stacks, arXiv:math.DG/0405003, Compositio Mathematica, Volume 142 (2006), Issue 01, pp 251--270 link.

(with Chenchang Zhu) Integrating Poisson manifolds via stacks, arXiv:math.DG/0411370, Travaux Mathématiques, Volume 16 (2005), 285--297 journal link.

Birational Geometry

(with Jiun-Cheng Chen) Cone Theorem via Deligne-Mumford stacks, arXiv:math.AG/0505043, Mathematische Annalen, Volume 345 (2009), no. 3, 525--545 link.

(with Jiun-Cheng Chen) Note on characterizations of projective spaces, arXiv:math.AG/0509649, Communications in Algebra, Volume 35 (2007), Issue 11, 3808--3819 link.

(with Jiun-Cheng Chen) Simple Grassmannian flops, arXiv:2410.22668, submitted.

Derived Categories

(with Jiun-Cheng Chen) A note on derived McKay correspondence, arXiv:math.AG/0609737, Mathematical Research Letters, Volume 15 (2008), Issue 3, 435--445 link.

(with Qian Chao and Jiun-Cheng Chen) On the derived category of a toric stack bundle, arXiv:2407.21288, Journal of Pure and Applied Algebra 229, No. 2, Article ID 107882, 8 p. (2025) link.

(with Jiun-Cheng Chen) On the derived category of a weighted blowup, submitted.

Chen-Ruan orbifold cohomology and related topics

(with Yunfeng Jiang) The orbifold Chow ring of hypertoric Deligne-Mumford stacks, arXiv:math.AG/0512199, Journal für die reine und angewandte Mathematik (Crelle's Journal), Volume 2008, Issue 619, Pages 175--202 link.

(with Yunfeng Jiang) Note on orbifold Chow rings of semi-projective toric Deligne-Mumford stacks, arXiv:math.AG/0606322, Communications in Analysis and Geometry, Volume 16 (2008), Number 1, 231--250 link.

(with Markus J. Pflaum, Hessel Posthuma, and Xiang Tang) Orbifold cup products and ring structures on Hochschild cohomologies, arXiv:0706.0027, Communications in Contemporary Mathematics, Volume 13, Issue 1 (2011), 123--182 link.

(with Yunfeng Jiang) The Integral (orbifold) Chow Ring of Toric Deligne-Mumford Stacks, arXiv:0707.2972, Mathematische Zeitschrift, Volume 264, Number 1 (2010), 225--248 link.

(with Yunfeng Jiang) On the K-theory of Toric Stack Bundles, arXiv:0808.1754, Asian Journal of Mathematics 14 (2010), no. 1, 1--10 link.

High energy physics

(with Herb Clemens, Joseph Marsano, Tony Pantev, and Stuart Raby) A Global SU(5) F-theory model with Wilson line breaking, arXiv:1206.6132, Journal of High Energy Physics (2013) 150, link.