Changzheng Li
About me
I am currently working in the School of Mathematics of Sun Yat-sen University in Guangzhou in China. Prior to that, I was an IBS Fellow at IBS-CGP on the campus of POSTECH for two years. As a postdoctoral researcher, I spent three years at Kavli IPMU, University of Tokyo and spent two years at KIAS, where my mentor was Professor Bumsig Kim .
I got my PhD from the IMS and Department of Mathematics at Chinese University of Hong Kong in July 2009, under the guidance of Professor Naichung Conan Leung. I spent my undergraduate years at University of Science and Technology of China .
Here is my Curriculum Vitae.
Contact me:
School of Mathematics,Sun Yat-sen Unviersity,Xingangxi Road 135, Haizhu, Guangzhou, 510275, China
Office: Room 815
Phone: +86-20-8411-1738
Email: lichangzh AT mail.sysu.edu.cn
Research
Research Insterests
I am interested in Algebraic Geometry, Kahler Geometry, with special emphasis on Gromov-Witten theory and Quantum Schubert Calculas. Currently, I am particularly interested in the following topics:
1) Quantum K-theory of flag varieties.
2) Mirror symmetry for flag varieties.
3) Primitive forms and Landau-Ginzburg B-model.
4) Conjecture O and Gamma Conjecturs by Galkin-Golyshev-Iritani.
Preprints and work in progress
- (with N.-C. Leung) Appendix to the paper "Functorial relationships between QH^*(G/B) and QH^*(G/P)".
- (with S. Li and K. Saito) Primitive forms via polyvector fields, preprint at arxiv: math.AG/1311.1659.
- (with Konstanze Rietsch, Mingzhi Yang and Chi Zhang), A Plucker coordinate mirror for partial flag varieties and quantum Schubert calculus, preprint at arXiv: math.AG/2401.15640.
- (with Sergey Galkin, Jianxun Hu, Hiroshi Iritani, Hua-Zhong Ke and Zhitong Su), Revisiting Gamma conjecture I: counterexamples and modifications, preprint at arXiv: math.AG/2405.16979.
- (with Jianxun Hu,Hua-Zhong Ke and Lei Song), Mirror symmetry for certain blowups of Grassmannians, preprint at arXiv: math.AG/2502.13545.
- (with Thorgal Hinault, Tony Yue YU, Chi Zhang and Shaowu Zhang ), Unfolding of equivariant F-bundles and application to the mirror symmetry of flag varieties, preprint at arXiv: math.AG/2505.09950.
- (with Konstanze Rietsch and Mingzhi Yang), An anticanonical perspective on G/P Schubert varieties, preprint at arXiv: math.AG/2506.18388.
- (with Hua-Zhong Ke and Jiayu Song), Towards small quantum Chern character, preprint at arXiv: math.AG/2507.12333.
Conference proceeding
- (Editors: Kentaro Hori, Changzheng Li, Si Li, Kyoji Saito) Primitive Forms and Related Subjects — Kavli IPMU 2014, Adv. Stud. Pure Math., 83, The Mathematical Society of Japan, 2019.
- (Editors: Jianxun Hu, Changzheng Li, Leonardo C. Mihalcea) Schubert Calculus and Its Applications in Combinatorics and Representation Theory, Springer Proceedings in Mathematics & Statistics vol. 332, Springer, 2020.
Accepted/Published papers (Pdf files here may be slightly different from the published version)
- (with N.-C. Leung) Hard Lefschetz actions in Riemannian geometry with special holonomy. Math. Res. Lett. 15 (2008), no. 4, 683-698.
- (with N.-C. Leung) Functorial relationships between QH^*(G/B) and QH^*(G/P). J. Differential Geom. 86 (2010), no. 2, 303-354.
- (with N.-C. Leung) Gromov-Witten invariants for G/B and Pontryagin product for OmegaK. Tran. Amer. Math. Soc. (2012) no. 5, 2567-2599.
- (with N.-C. Leung) Classical aspects of quantum cohomology of generalized flag varieties. Int. Math. Res. Not. IMRN (2012), no. 16, 3706-3722.
- (with N.-C. Leung) Quantum Pieri rules for tautological subbunldes, Adv. Math. 248 (2013), 279-307.
- (with L.C. Mihalcea) K-theoretic Gromov-Witten invariants of lines in homogeneous spaces. Int. Math. Res. Not. IMRN (2014), no. 17, 4625-4664.
- Functorial relationships between QH^*(G/B) and QH^*(G/P) (II). Asian J. Math. 19 (2014), no.2, 203-234.
- (with Y. Huang) On equivariant quantum Schubert calculus for G/P, J. Algebra 441 (2015), 21–56.
- (with V. Ravikumar) Equivariant Pieri rules for isotropic Grassmannians, Math. Ann. 365 (2016), no. 1-2, 881–909.
- (with D. Cheong) On the Conjecture O for G/P, Adv. Math. 306 (2017), 704--721.
- (with S. Li, K. Saito and Y. Shen) Mirror symmetry for exceptional unimodular singularities, J. Eur. Math. Soc.19 (2017), no. 4, 1189–1229. (Codes for the four-point functions in the appendix: .nb file via mathematica or pdf file).
- (with N.-C. Leung) An update of quantum cohomology of homogeneous varieties, Proceedings of the Sixth International Congress of Chinese Mathematicians. Vol. II, 211–235, Adv. Lect. Math. (ALM), 37, Int. Press, Somerville, MA, 2017.
- (with T. Lam, L. Mihalcea and M. Shimozono) A conjectural Peterson isomorphism in K-theory, J. Algebra 513 (2018), 326–343.
- (with V. Ravikumar, F. Sottile and M. Yang) A geometric proof of an equivariant Pieri rule for flag manifolds, Forum Math. 31 (2019), no. 3, 779–783.
- (with L. Mihalcea and R. Shifler) On the Conjecture O for odd symplectic Grassmannians, Bull. London Math. Soc. 51, (2019), 705–714.
- (with K. Chan and N.C. Leung) Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties, J. Geom. Phys. 146 (2019), 103489.
- (with A.S. Buch, S. Chung and L. Mihalcea) Euler characteristics in the quantum K-theory of flag varieties, Selecta Math. (N.S.) 26 (2020), no. 2, 29.
- (with J.Hu, H.-Z. Ke, and T. Yang) Gamma conjecture I for del Pezzo surfaces, Adv. Math. 386 (2021), 107797.
- (with D. Hwang, H. Lee, and J.-H. Lee) W-translated Schubert divisors and transversal intersections, Sci. China Math. 65 (2022), no. 10, 1997–2018.
- (with R. Shifler, M. Yang and C. Zhang) On Frobenius-Perron dimension, Proc. Amer. Math. Soc. 150 (2022), no. 12, 5035–5045.
- (with F. Sottile and C. Zhang) On the fundamental group of open Richardson varieties, Commun. Number Theory Phys. 17 (2023), no. 1, 77–101.
- (with Haoqiang Hu and Zhaoyang Liu) Effective good divisibility of rational homogeneous varieties, Math. Z. 305 (2023), no. 3, 52.
Codes for Grassmannians of exceptional type by Mathematica 10.0: nb file via mathematica or pdf file of output). - (with Jianxun Hu, Hua-Zhong Ke and Lei Song) On the quantum cohomology of blow-ups of four-dimensional quadrics, Acta Math. Sin. (Engl. Ser.) 35 (2024), no. 1, pp. 313–328.
- (with Changjian Su and Rui Xiong) Automorphisms of the Quantum Cohomology of the Springer Resolution and Applications, Adv. Math. 442 (2024), 109577.
- (with Jiayu Song), Toward the quantum Pieri rule for Fl_n via Seidel representation (in Chinese), SCIENTIA SINICA Mathematica, 2024, 54(12): 2009–2022. (English translation available here)
- (with Jianxun Hu, Hua-Zhong Ke and Zhitong Su), On Galkin's Lower Bound Conjecture, Asian J. Math. 28 (2025), no. 4, 609–616.
- (with Zhaoyang Liu, Jiayu Song and Mingzhi Yang) On Seidel representation in quantum $K$-theory of Grassmannians, Sci. China Math. 68 (2025), no. 7, 1523–1548.
Teaching
Teaching experience
Spring 2023: Algebra
Announcement:
General Information
Lecturer: LI, Changzheng 李长征
Office: New Math. Building 815
Tel: 8411 1738
Email: lichangzh AT mail.sysu.edu.cn
Office Hour: by appointment.
Time and Venue
Lecture:
Venue: ;
Course Description
This course is an introduction to
Topics include:
Event (to be updated)