*Higher genus quantum K-theory*, (with**You-Cheng Chou**and**Leo Herr**), arXiv:2305.10137.*Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero*, (with**You-Cheng Chou**), arXiv:2305.08480.-
*Gopakumar-Vafa Invariants = Quantum K-invariants on Calabi-Yau threefolds*, (with**Y.-C. Chou**), arXiv:2212.13432, Bumsig Kim Memorial Volume -
*Quantum K-invariants and Gopakumar-Vafa invariants I. The quintic threefold*, (with**Y.-C. Chou**), arXiv:2211.00788. -
*The Log Product Formula in quantum K-theory*, (with**Y.-C. Chou and L. Herr**), arXiv:2012.09379, to be published in Math. Proc. Cambridge Philos. Soc. *Quantum flips I: local model*, (with**H.-W. Lin and C.-L. Wang**), arXiv:1912.03012, Boris Dubrovin Memorial Volume.*Virasoro constraints for moduli of weighted pointed stable curves*(with**Y.-C. Chou**), arxiv:1908.09027.*Variations on the theme of quantum Lefschetz*(with**H. Fan**), arXiv:1812.01732.*Towards a quantum Lefschetz hyperplane theorem in all genera*(with**H. Fan**), arXiv:1712.03573.*Quantum Cohomology under Birational Maps and Transitions*, (with**H.-W. Lin and C.-L. Wang**), arXiv:1705.04799.*A product formula for log Gromov--Witten invariants*, (with**F. Qu**), arXiv:1701.04527.*On Gromov-Witten theory of projective bundles*, (with**H. Fan**), arXiv:1607.00740.*Towards A + B theory in conifold transitions*, (with**H.-W. Lin and C.-L. Wang**), arXiv:1502.03277.*A proof of the Landau-Ginzburg/Calabi-Yau correspondence via the crepant transformation conjecture*(with**N. Priddis and M. Shoemaker**), arXiv:1410.5503.*Invariance of quantum rings under ordinary flops: III*, (with**H.-W. Lin, F. Qu and C.-L. Wang**), arXiv:1401.7097.*Invariance of quantum rings under ordinary flops: II*, (with**H.-W. Lin and C.-L. Wang**), arXiv:1311.5725.*Invariance of quantum rings under ordinary flops: I*, (with**H.-W. Lin and C.-L. Wang**), arXiv:1109.5540.*A Mirror Theorem for the Mirror Quintic*, (with**M. Shoemaker**), arXiv:1209.2487, to appear in Geometry and Topology.*Euler characteristics of universal cotangent line bundles on $\Mbar_{1,n}$*(with**F. Qu**), arXiv:1211.2450, to appear in proceedings of the AMS.*Introduction to GWT and CTC*, my notes from Grenoble Lectures in the summer 2011.*Analytic continuations of quantum cohomology*, (with**H.-W. Lin and C.-L. Wang**), to appear in proceedings ICCM 2010.*Algebraic cobordism of bundles on varieties*(with**R. Pandharipande**) arXiv:1002.1500, to appear in JEMS.*Algebraic structures on the topology of moduli spaces of curves and maps*(with**R. Vakil**), arXiv:0809.1879, to appear in Surveys in Differential Geometry.*Invariance of Gromov--Witten theory under a simple flop*(with**Y. Iwao, H.-W. Lin and C.-L. Wang**), arXiv:0804.3816, to appear in Crelle's.*The quantum orbifold cohomology of weighted projective spaces*(with**T. Coates, A. Corti, and H.-H. Tseng**), math.AG/0608481, Acta Mathematica 202 (2009) no. 2.*Flops, motives and invariance of quantum rings*(with**H.-W. Lin and C.-L. Wang**) (final version 30 June 2006) math.AG/0608370, Annals of Math, 172 (2010) no.1 243-290.*On independence of generators of the tautological rings*(with**D. Arcara**), math.AG/0605488, Compositio Math 144 (2008) no. 6 1497--1503.*Notes on axiomatic Gromov--Witten theory and applications*, arXiv:0710.4349, Algebraic geometry---Seattle 2005. Part 1, 309--323, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009.*Invariance of tautological equations II: Gromov--Witten theory*, (**Appendix with Y. Iwao**,) math.AG/0605708, JAMS 22 (2009) no. 2, 331-352.

**New!**An exciting consequence of ITE2 has just come out. In math.AG/0612510 by**Faber, Shadrin, and Zvonkine, they solved Witten's r-spin conjecture completely**. In fact, that was the original motivation of ITE project, which we were not able to carry through....*Invariance of tautological equations I: conjectures and applications*, math.AG/0604318, J Euro Math Soc 10 (2008) no. 2, 399-413.*Tautological equations in \Mbar_{3,1} via invariance conjectures*(with**D. Arcara**). math.AG/0503184. updated version. To appear in Canadian Journal of Mathematics.*Tautological equations in genus 2 via invariance conjectures*(with**D. Arcara**), math.AG/0502488. updated version.*Witten's conjecture, Virasoro conjecture, and invariance of tautologicalequations*, math.AG/0311100.*Witten's conjecture and Virasoro conjecture up to genus two*, math.AG/0310442. To appear in the proceedings of the conference "Gromov-Witten Theory of Spin Curves and Orbifolds", Contemp. Math., AMS.*Quantum K-Theory II: Computations and open problems*, in preparation.*Frobenius manifolds, Gromov--Witten theory, and Virasoro constraints*, (with**R. Pandharipande**), a book in preparation, Part1.ps, Part2.ps (partial), (Part 3 not yet available).*A reconstruction theorem in quantum cohomology and quantum K-theory*, (with**R. Pandharipande**), math.AG/0104084. Updated PDF file. Amer. J. Math., 126 (2004), no. 6, 1367--1379.*Quantum K-theory on flag manifolds, finite difference Toda lattices and quantum groups*(with**A. Givental**), Invent. Math.**151**, 193-219, 2003. math.AG/0108105, Link to the published version.*Quantum K-Theory I: Foundations*, math.AG/0105014. Duke Math. J. 121 (2004), no. 3, 389-424, Link.*Virtual Fundamental Classes of Zero Loci*, (with**D. Cox and S. Katz**), in "Advances in algebraic geometry motivated by physics" (Lowell, MA, 2000), 157--166, Contemp. Math., 276, Amer. Math. Soc., Providence, RI, 2001. math.AG/0006116.*Quantum Lefschetz hyperplane theorem*, Invent. Math. 145 (2001), no. 1, 121--149. math.AG/0003128. Link to the published version.*A formula for Euler characteristics of tautological line bundles on the Deligne-Mumford spaces*, IMRN 1997 No. 8. PDF.*Quantum K-theory*, PhD thesis, UC Berkeley, 1999.*The quadrupole moment of Delta and Hyperion calculated on the constituent quark shell model in large oscillator basis*, (with**W.-C. Chang**), B.S. thesis, communicated in the annual meeting of Taiwanese physical society, 1991.

- Algebraic Geometry Group
- Algebraic Geometry Seminar
- String Geometry Seminar
- Research page of the mathematics department. (outdated!)
- OSP at U Conflict of interest form Travel administration

- NSF (Links: DMS, Fastlane, research.gov)
- AMS Centennial Fellowship (2005-2007).