Links to research papers in pdf

Last update: January 17, 2020

Papers on arXiv, on MathSciDoc, reviewed in AMS MathSciNet .

• [*] A blow-up formula in GW theory, (with Y.-P. Lee and H.-W. Lin) work in progress.
• [pdf] Algebraic methods in periodic singular Liouville equations, in "Proceeding of the International Consortium of Chinese Mathematicians 2017", International Press 2021, Boston, 51–101.
• [pdf] Quantum flips I: local model, (with Y.-P. Lee and H.-W. Lin), in "Integrability, Quantization, and Geometry II (Dubrovin memorial volume)", AMS Proceedings of Symposia in Pure Mathematics 103.2 (2021), 303–352. arXiv:1912.03012.
• [pdf] Geometric quantities arising from bubbling analysis of mean field equations, (with C.-S. Lin), Comm. Anal. Geom. 28 (2020), no. 6, 1289–1313 arXiv:1609.07204.
• [pdf] Aspects on Calabi–Yau moduli, in "Proceeding of Uniformizations, Riemann–Hilbert correspondence, Calabi–Yau manifolds, and Picard–Fuchs equations, Mittag–Leffler Institute 2015", Advanced Lectures in Mathematics 42 (2018), 529–552.
• [pdf] Towards A + B theory in conifold transitions for Calabi–Yau threefolds, (with Y.-P. Lee and H.-W. Lin), J. Differential Geometry 110 (2018), no. 3, 495–541, arXiv:1502.03277.
• [pdf] Green function, Painlevé VI equation, and Eisenstein series of weight one, (with Z. Chen, T.-J. Kuo and C.-S. Lin), J. Differential Geometry 108 (2018), 185–241.
• [pdf] Quantum cohomology under birational maps and transitions, (with Y.-P. Lee and H.-W. Lin), in "Proceedings of the String-Math Conference 2015 at TSIMF, Sanya", AMS Proceedings of Symposia in Pure Mathematics 96 (2017), 149–168. arXiv:1705.04799.
• [pdf] On the minimality of extra critical points of Green functions on flat tori, (with C.-S. Lin), Int. Math. Res. Notices (2017), no. 18, 5591–5608.
• [pdf] Mean field equations, hyperelliptic curves and modular forms II, with an appendix by Y.-C. Chou, (with C.-S. Lin), Journal de l’École polytechnique – Mathématiques 4 (2017), 557–593. arXiv:1502.03295.
• [pdf] Invariance of quantum rings under ordinary flops III: A quantum splitting principle, (with Y.-P. Lee, H.-W. Lin and F. Qu), Cambridge J. of Math. 4 (2016), no. 3, 333–401. arXiv:1401.7097.
• [pdf] Invariance of quantum rings under ordinary flops II: A quantum Leray–Hirsch theorem, (with Y.-P. Lee and H.-W. Lin), Algebraic Geometry 3 (2016), no. 5, 615–653. arXiv:1311.5725.
• [pdf] Invariance of quantum rings under ordinary flops I: Quantum corrections and reduction to local models, (with Y.-P. Lee and H.-W. Lin), Algebraic Geometry 3 (2016), no. 5, 578–614. arXiv:1109.5540. (Here for the original combined version.)
• [pdf] Mean field equations, hyperelliptic curves and modular forms I, (with C.-L. Chai and C.-S. Lin), Cambridge J. of Math. 3 (2015), no. 1–2, 127–274. arXiv:1502.03297.
• [pdf] Invariance of Gromov–Witten theory under a simple flop, (with Y. Iwao, Y.-P. Lee and H.-W. Lin), J. reine angew. Math. 663 (2012), 67–90. arXiv:0804.3816.
• [pdf] Analytic continuations on quantum cohomology, in "Proceeding of the Fifth International Congress of Chinese Mathematicians, Beijing 2010", AMS/IP Studies in Advanced Mathematics 51 (2012), 269–282.
• [pdf] Extensions of multiply twisted pluri-canonical forms, (with C.-Y. Chi and S.-S. Wang), Pure Appl. Math. Quarterly 7 (2011), no. 4, 1129–1164. arXiv:1101.2077.
• [pdf] Quantum invariance under flop transitions, in "Geometric Analysis: Present and Future", Adv. Lect. Math. 18 (2010), 347–370.
• [pdf] A function theoretic view of the mean field equations on tori, (with C.-S. Lin), Adv. Lect. Math. 11 (2010), 173–193.
• [pdf] Elliptic functions, Green functions and the mean field equations on tori, (with C.-S. Lin), Annals of Math. 172 (2010), no. 2, 911–954. arXiv:math/0608358.
• [pdf] Flops, motives and invariance of quantum rings, (with Y.-P. Lee and H.-W. Lin), Annals of Math. 172 (2010), no. 1, 243–290. arXiv:math/0608370.
• [pdf] Motivic and quantum invariance under stratified Mukai flops, (with B. Fu), J. Differential Geometry 80 (2008), no. 2, 261–280. arXiv:0801.3551.
• [pdf] K-equivalence in birational geometry, in "Proceeding of the Second International Congress of Chinese Mathematicians, Taipei 2001", New Stud. Adv. Math. 4 (2004), 199–216. arXiv:math/0204160.
• [pdf] Curvature properties of the Calabi–Yau moduli, Documenta Mathematica 8 (2003), 577–590.
• [pdf] Quasi-Hodge metrics and canonical singularities, Math. Res. Lett. 10 (2003), 57–70. arXiv:math/0211456.
• [pdf] K-equivalence in birational geometry and characterizations of complex elliptic genera, J. Algebraic Geometry 12 (2003), no. 2, 285–306. arXiv:math/0103063.
• [pdf] Cohomology theory in birational geometry, J. Differential Geometry 60 (2002), no. 2, 345–354.
• [pdf] Weak Lefschetz principle is false for ample cone, (with B. Hassett and H.-W. Lin), Asian J. of Math. 6 (2002), 95–100.
• [pdf] On the topology of birational minimal models, J. Differential Geometry 50 (1998), no. 1, 129–146. arXiv:math/9804050.
• [pdf] On the incompleteness of the Weil–Petersson metric along degenerations of Calabi–Yau manifolds, Math. Res. Lett. 4 (1997), 157–171. (Here for the update of section 3 from my 1998 Dissertation concerning non-trivial monodromy.)