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
Seminars