Yang, Di (杨迪)
Full Professor, USTC
School of Mathematical Sciences
University of Science and Technology of China
Hefei 230026, P.R. China
Office: 1627
Tel.: + 86 - 0551-63603909
E-mail: diyang@ustc.edu.cn
- August 2004 -- July 2008, B.Sc., Tsinghua University, Beijing
- August 2008 -- July 2013, Ph.D., Tsinghua University, Beijing (Oct. 2009 -- Oct. 2010 in visiting University of Cambridge, and Sep. 2012 -- Dec. 2012 in visiting SISSA)
- September 2013 -- September 2016, post-doc, SISSA, Trieste
- September 2016 -- August 2018, post-doc, MPIM, Bonn
- September 2018 -- August 2023, professor under a China innovation talent program for young people, USTC, Hefei
- September 2023 -- , full professor, USTC, Hefei
Research Interest
- Frobenius manifolds, moduli space of curves, and Gromov--Witten type invariants
- hodographs for PDEs of hydrodynamic type, and the Dubrovin--Zhang normal forms
- geometry and arithmetic of integrable systems
- applications of Lie algebras and vertex algebras
- quantum integrable systems and modular forms
Selected Publications (including arXiv preprints)
47. (with C. Zhang and Z. Zhou) On an infinite commuting ODE system associated to a simple Lie algebra. arXiv:2404.16458
46. (with J. Xu) Galilean symmetry of the KdV hierarchy. arXiv:2403.04631
45. (with D. Valeri) Remarks on intersection numbers and integrable hierarchies. II. Tau-structure. arXiv:2312.16575
44. (with J. Zhou) From Toda hierarchy to KP hierarchy. arXiv:2311.06506
43. Analytic theory of Legendre-type transformations for a Frobenius manifold. to appear in Communications in Mathematical Physics. arXiv:2311.04200
42. (with D. Zagier) Mapping partition functions. arXiv:2308.03568
41. (with A. Fu and D. Zuo) The constrained KP hierarchy and the bigraded Toda hierarchy of (M, 1)-type. Lett. Math. Phys., 113 (2023), Paper No. 124, 44 pp. (LMP) arXiv:2306.09115
40. GUE Via Frobenius manifolds. II. Loop equations. arXiv:2407.19170
39. (with Q. Zhang) On a new proof of the Okuyama--Sakai conjecture. Rev. Math. Phys., 35 (2023), Paper No. 2350025. (RMP) arXiv:2303.09243
38. (with A. Fu and M. Li) From wave functions to tau-functions for the Volterra lattice hierarchy. Acta Math. Sci. Ser. B (Engl. Ed.), 44 (2024), 405-–419. (AMScientia)
37. Degree zero Gromov--Witten invariants for smooth curves. Bull. Lond. Math. Soc., 56 (2024), 96-110. (BLMS) arXiv:2208.02095
36. GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back. Acta Mathematica Sinica (English Series), 40 (2024), 383–-405. (AMSinica) arXiv:2205.01618
35. (with J. Zhou) Grothendieck's Dessins d'Enfants in a Web of Dualities. III. Journal of Physics A: Mathematical and Theoretical, 56 (2023), Paper No. 055201. (JPA) arXiv:2204.11074
34. (with S.-Q. Liu, Y. Zhang and C. Zhou) On Equivariant Gromov--Witten Invariants of Resolved Conifold with Diagonal and Anti-Diagonal Actions. Letters in Mathematical Physics, 112 (2022), Paper No. 129. (LMP) arXiv:2203.16812
33. (with A. Fu) The matrix-resolvent method to tau-functions for the nonlinear Schrödinger hierarchy. Journal of Geometry and Physics, 179 (2022), Paper No. 104592. (JGP) arXiv:2201.11020
32. (with C. Zhou) Gelfand--Dickey hierarchy, generalized BGW tau-function, and W-constraints. Nonlinearity, 36 (2023), 1873--1889. (NL) arXiv:2112.14595
31. (with M. Cafasso) Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method. Journal of Physics A: Mathematical and Theoretical, 55 (2022), Paper No. 204001. (JPA) arXiv:2112.14202
30. (with Q. Zhang) On the Hodge-BGW correspondence. Communications in Number Theory and Physics, 18 (2024), 611--651. (CNTP) arXiv:2112.12736
29. (with S.-Q. Liu, Y. Zhang and J. Zhou) The Virasoro-like Algebra of a Frobenius Manifold. IMRN, 2023, 13524--13561. (IMRN) arXiv:2112.07526
28. (with J. Guo) On the large genus asymptotics of psi-class intersection numbers. Math. Ann., 388 (2024), 61–97. (MA) arXiv:2110.06774
27. (with B. Dubrovin and D. Valeri) Affine Kac--Moody algebras and tau-functions for the Drinfeld--Sokolov hierarchies: The matrix-resolvent method. SIGMA 18 (2022), 077, 32 pages. (SIGMA) arXiv:2110.06655
26. (with G. Ruzza) On the spectral problem of the quantum KdV hierarchy. Journal of Physics A: Mathematical and Theoretical, 54 (2021), Paper No. 374001. (JPA) arXiv:2104.01480
25. (with B. Dubrovin and D. Zagier) Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality. Advances in Mathematics, 433 (2023), paper no. 109311. (AM) arXiv:2101.10924
24. (with C. Zhou) On an extension of the generalized BGW tau-function. Letters in Mathematical Physics, 111 (2021), paper no. 123. (LMP) arXiv:2010.00436
23. (with D. Zagier and Y. Zhang) Masur--Veech volumes of quadratic differentials and their asymptotics. Journal of Geometry and Physics, 158 (2020), paper no. 103870. (JGP) arXiv:2005.02275
22. Hamiltonian perturbations at the second order approximation. Annales Henri Poincar\'e, 21 (2020), 3919-–3937. (AHP) arXiv:2002.00823
21. (with S.-Q. Liu, Y. Zhang and C. Zhou) The Hodge-FVH Correspondence. Journal für die reine und angewandte Mathematik, 775 (2021), 259--300. (Crelle) arXiv:1906.06860
20. On tau-functions for the Toda lattice hierarchy. Letters in Mathematical Physics, 110 (2020), 555--583. (LMP) arXiv:1905.08140
19. (with B. Dubrovin) Remarks on intersection numbers and integrable hierarchies. I. Quasi-triviality. Adv. Theo. Math. Phys., 24 (2020), 1055--1085. (ATMP) arXiv:1905.08106
18. (with B. Dubrovin) Matrix resolvents and the discrete KdV hierarchy. Comm. Math. Phys., 377 (2020), 1823–-1852. (CMP) arXiv:1903.11578
17. (with B. Dubrovin and D. Zagier) On tau-functions for the KdV hierarchy. Selecta Mathematica, 27 (2021), paper number 12. (SM) arXiv:1812.08488
16. (with S.-Q. Liu, Y. Zhang and C. Zhou) The Loop Equation for Special Cubic Hodge Integrals. Journal of Differential Geometry, 121 (2022), 341–-368. (JDG) arXiv:1811.10234
15. (with B. Dubrovin and D. Zagier) Gromov--Witten invariants of the Riemann sphere. Pure and Applied Mathematics Quarterly, 16 (2020), 153--190. (PAMQ) arXiv:1802.00711
14. (with M. Cafasso and A. du C. de Villeneuve) Drinfeld-Sokolov hierarchies, tau functions, and generalized Schur polynomials. SIGMA, 14 (2018), paper no. 104. (SIGMA) arXiv:1709.07309
13. (with B. Dubrovin and D. Zagier) Classical Hurwitz number and related combinatorics. Moscow Mathematical Journal, 17 (2017), 601--633. (MMJ)
12. (with B. Dubrovin) On Gromov--Witten invariants of P^1. Mathematical Research Letters, 2019, 26, 729--748. (MRL) arXiv:1702.01669
11. (with B. Dubrovin, S.-Q. Liu and Y. Zhang) Hodge-GUE correspondence and the discrete KdV equation. Comm. Math. Phys., 379 (2020), 461--490. (CMP) arXiv:1612.02333
10. (with M. Bertola and B. Dubrovin) Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions. Mosc. Math. J., 21 (2021), 233--270. (MMJ) arXiv:1610.07534
9. (with B. Dubrovin) On cubic Hodge integrals and random matrices. Communications in Number Theory and Physics, 2017, 11, 311--336. (CNTP) arXiv:1606.03720
8. (with B. Dubrovin) Generating series for GUE correlators. Letters in Mathematical Physics, 2017, 107, 1971--2012. (LMP) arXiv:1604.07628
7. (with M. Bertola and B. Dubrovin) Simple Lie algebras and topological ODEs. IMRN, 2018, 1368--1410. (IMRN) arXiv:1508.03750
6. (with M. Bertola and B. Dubrovin) Correlation functions of the KdV hierarchy and applications to intersection numbers over \M_{g,n}. Physica D: Nonlinear Phenomena, 327 (2016), 30--57. (PDNP) arXiv:1504.06452
5. (with F. Balogh) Geometric interpretation of Zhou's explicit formula for the Witten--Kontsevich tau function. Letters in Mathematical Physics, 2017, 107, 1837--1857. (LMP) arXiv:1412.4419
4. (with M. Bertola) The partition function of the extended r-reduced Kadomtsev--Petviashvili hierarchy. Journal of Physics A: Mathematical and Theoretical, 48 (2015), paper no. 195205. (JPA) arXiv:1411.5717
3. (with B. Dubrovin, S.-Q. Liu and Y. Zhang) Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Advances in Mathematics, 293 (2016), 382--435. (AM) arXiv:1409.4616
2. (with S.-Q. Liu and Y. Zhang) Uniqueness Theorem of W-Constraints for Simple Singularities. Letters in Mathematical Physics, 103 (2013), 1329--1345. (LMP) arXiv:1305.2593
1. (with A.S. Fokas) On a novel class of integrable ODEs related to the Painlev\'e equations. International Journal of Bifurcation and Chaos, 22 (2012), paper no. 1250211. (IJBC) arXiv:1009.5125
Editorship
- Journal of Nonlinear Mathematical Physics
Selected Invited Talks
-
International Congress of Chinese Mathematicians, July 31--August 5, 2022, Nanjing, China
Integrable Systems in Geometry and Mathematical Physics, Conference in Memory of Boris Dubrovin, SISSA, June 26--July 2, 2021, Trieste, Italy (virtual)
Conference Integrability and Randomness in Geometry and Mathematical Physics, CIRM, April 8--12, 2019, Luminy, France
Annual Meeting of Chinese Mathematical Society, October 19--21, 2018, Guiyang, China
90's Anniversary of Tsinghua Mathematics, Tsinghua University, April 21--24, 2017, Beijing, China
Moduli Spaces in Algebraic Geometry and Mathematical Physics, Chern Institute, September 18--22, 2015, Tianjin, China
Teachings
- 2024 春, Linear Algebra (线性代数), Tuesday 1-2 and Thursday 3-4, USTC.
- 2023 秋, Topics in Integrable Systems (可积系统选讲), USTC.
- 2023 春, Complex Analysis (复分析), USTC.
- 2022 秋, Differential Geometry (微分几何), USTC
- 2022 春, Theory of Integrable Systems (可积系统理论), USTC
- 2021 秋, Differential Geometry (微分几何), USTC
- 2021 春, Complex Analysis (复分析), USTC
- 2020 秋, Theory of Integrable Systems (可积系统理论), USTC
- 2020 春, Complex Analysis (复分析), USTC
- 2019 秋, Differential Geometry (微分几何), USTC
- 2019 春, Linear Algebra (线性代数), USTC
- 2018 秋, Modern Mathematical Physics Problems (现代数学物理问题), USTC
- 2018 Spring, Introduction to Integrable Systems, MPIM
- 2017 Spring, Frobenius Manifolds, MPIM
- 2016 Spring, Introduction to Frobenius Manifolds, SISSA
- Other courses: 华罗庚讨论班 (2021-2022, USTC), 科学与社会研讨课 (2019 - 2020, 2020 - 2021, 2023 - 2024, 2024 - , USTC), 纯粹数学前沿 (2020 summer, USTC)
Scientific Visits
- Tsinghua University, Beijing, July 2013 - August 2013
- Concordia University, Montreal, October 2014 - November 2014
- MPIM, Bonn, July 2019 - August 2019
- MPIM, Bonn, July 2023
- MPIM, Bonn, August 2024