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 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. 
• (with  Sergey Galkin，Naichung Conan Leung and Rui Xiong), A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology， preprint at arXiv: math.AG/2509.01101; with an appendix by Pieter Belmans and Markus Reineke. 
• (with   Jianxun Hu, Hua-Zhong Ke and Zhitong Su), Gamma conjecture II via global Gamma-I， preprint at arXiv: math.AG/2606.07418.
• (with Konstanze Rietsch and Mingzhi Yang), A Peterson program for general Schubert varieties and mirror symmetry, preprint at arXiv: math.AG/2609.30242.

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)

1. (with N.-C. Leung) Hard Lefschetz actions in Riemannian geometry with special holonomy. Math. Res. Lett. 15 (2008), no. 4, 683-698.
2. (with N.-C. Leung) Functorial relationships between QH^*(G/B) and QH^*(G/P).  J. Differential Geom. 86 (2010), no. 2, 303-354.
3. (with N.-C. Leung) Gromov-Witten invariants for G/B and Pontryagin product for OmegaK. Trans. Amer. Math. Soc. (2012) no. 5, 2567-2599.
4. (with N.-C. Leung) Classical aspects of quantum cohomology of generalized flag varieties. Int. Math. Res. Not. IMRN (2012), no. 16, 3706-3722.
5. (with N.-C. Leung) Quantum Pieri rules for tautological subbunldes, Adv. Math. 248 (2013), 279-307.
6. (with L.C. Mihalcea) K-theoretic Gromov-Witten invariants of lines in homogeneous spaces. Int. Math. Res. Not. IMRN (2014), no. 17, 4625-4664.
7.  Functorial relationships between QH^*(G/B) and QH^*(G/P) (II). Asian J. Math. 19 (2014), no.2, 203-234.
8. (with Y. Huang) On equivariant quantum Schubert calculus for G/P,  J. Algebra 441 (2015), 21–56.  
9. (with V. Ravikumar) Equivariant Pieri rules for isotropic Grassmannians,  Math. Ann. 365 (2016), no. 1-2, 881–909.
10. (with D. Cheong) On the Conjecture O for G/P,  Adv. Math. 306 (2017), 704--721.
11. (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).
12. (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. 
13. (with T. Lam, L. Mihalcea and M. Shimozono) A conjectural Peterson isomorphism in K-theory, J. Algebra 513 (2018), 326–343. 
14. (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.
15. (with L. Mihalcea and R. Shifler) On the Conjecture O for odd symplectic Grassmannians,  Bull. London Math. Soc. 51, (2019),  705–714.
16. (with K. Chan and N.C. Leung) Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties, J. Geom. Phys. 146 (2019), 103489.
17. (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.
18. (with J.Hu, H.-Z. Ke,  and T. Yang) Gamma conjecture I for del Pezzo surfaces, Adv. Math. 386 (2021), 107797.
19. (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.
20. (with R. Shifler, M. Yang and C. Zhang) On Frobenius-Perron dimension,  Proc. Amer. Math. Soc. 150 (2022), no. 12, 5035–5045. 
21. (with F. Sottile and C. Zhang) On the fundamental group of open Richardson varieties, Commun. Number Theory Phys. 17 (2023), no. 1, 77–101.
22. (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). 
23. (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. 
24. (with Changjian Su and Rui Xiong)  Automorphisms of the Quantum Cohomology of the Springer Resolution and Applications, Adv. Math. 442 (2024), 109577.
25. (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)
26. (with Jianxun Hu, Hua-Zhong Ke and Zhitong Su), On Galkin's Lower Bound Conjecture,  Asian J. Math. 28 (2024), no. 4, 609–616.  
27. (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.
28. (with Jianxun Hu,Hua-Zhong Ke and Lei Song), Mirror symmetry for certain blowups of Grassmannians, to appear in Trans. Amer. Math. Soc. ; preprint at arXiv: math.AG/2502.13545.
29. (with   Jiayu Song，Rui Xiong and Mingzhi Yang), Quantum Schubert calculus for smooth Schubert divisors of Fln， to appear in Comm. Math. Phys. ; preprint at arXiv: math.AG/2509.17857.

Teaching

Teaching experience

Spring 2023:  Algebra

Announcement:

General Information

Lecturer: LI, Changzheng 李长征

Office: Zhenhuan Tang (震寰堂) A303

Tel: 3264 1924

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)