Yang, Di（杨迪）
Professor of Mathematics, USTC, Hefei
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
I received the PhD degree in Mathematics
from Tsinghua University in July, 2013.
My thesis advisor is Professor Youjin Zhang.
From September 2013 to August 2016, I was a post-doc at SISSA
under the supervision of Professor Boris Dubrovin.
From September 2016 to August 2018, I was a post-doc at MPIM
under the supervision of Professor Don Zagier.
Starting from September 2018 I'm a professor at School
of Mathematical Sciences, USTC.
Research Interests
- Frobenius manifolds and Gromov--Witten invariants
- Dubrovin--Zhang's normal form
- Moduli space of curves
- Geometry and arithmetic of integrable systems
- Lie algebras and vertex algebras
- Quantum integrable systems
Seminars - 2021, USTC
Current Teachings
Theory of Integrable Systems, USTC, Spring of 2022
华罗庚讨论班 (Seminars for Hua class), 2021-2022, USTC
Selected Publications
25. (with Chunhui Zhou)
On an extension of the generalized BGW tau-function. Letters in Mathematical Physics, 2021, to appear.
arXiv:2010.00436.
24. (with Giulio Ruzza) On the spectral problem of the quantum KdV hierarchy. Journal of Physics A., 2021, to appear.
arXiv:2104.01480.
23. (with Si-Qi Liu, Youjin Zhang and Chunhui Zhou)
The Hodge-FVH Correspondence. Journal für die reine und angewandte Mathematik.
Crelle.
22. Hamiltonian perturbations at the second order approximation. Annales Henri Poincar\'e.
(AHP)
21. (with Don Zagier and Youjin Zhang) Masur--Veech volumes of quadratic differentials and their asymptotics. Journal of Geometry and Physics, 2020, 158, paper number 103870, 12p.
(JGP)
20. (with Boris Dubrovin) Remarks on intersection numbers and integrable hierarchies. I. Quasi-triviality. Adv. Theo. Math. Phys., 2020.
arXiv:1905.08106.
19. On tau-functions for the Toda lattice hierarchy. Letters in Mathematical Physics, 2020, 110, 555--583.
(LMP)
18. (with Boris Dubrovin) Matrix resolvents and the discrete KdV hierarchy. Communications in Mathematical Physics, 2020, 377, 1823–-1852.
(CMP)
17. (with Boris Dubrovin and Don Zagier) On tau-functions for the KdV hierarchy. Selecta Mathematica, 2021, 27, paper number 12, 47p.
SM.
16. (with Si-Qi Liu, Youjin Zhang and Chunhui Zhou)
The Loop Equation for Special Cubic Hodge Integrals. Journal of Differential Geometry (to appear).
arXiv:1811.10234.
15. (with Boris Dubrovin and Don Zagier)
Gromov--Witten invariants of the Riemann sphere.
Pure and Applied Mathematics Quarterly, 2020, 16, 153--190. (PAMQ)
14. (with M. Cafasso and A. du Crest de Villeneuve)
Drinfeld-Sokolov hierarchies, tau functions, and generalized Schur polynomials.
SIGMA, 2018, 14, 104.
(SIGMA)
13. (with Boris Dubrovin and Don Zagier)
Classical Hurwitz number and related combinatorics.
Moscow Mathematical Journal, 2017, 17, 601--633.
(MMJ)
12. (with Boris Dubrovin) On Gromov--Witten invariants of P^1.
Mathematical Research Letters, 2019, 26, 729--748.
(MRL)
11. (with Boris Dubrovin, Si-Qi Liu and Youjin Zhang)
Hodge-GUE correspondence and the discrete KdV equation. Communications in Mathematical Physics, 379 (2020), 461--490.
(CMP)
10. (with Marco Bertola and Boris Dubrovin)
Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions. Moscow Mathematical Journal (to appear).
arXiv:1610.07534.
9. (with Boris Dubrovin) On cubic Hodge integrals and random matrices.
Communications in Number Theory and Physics, 2017, 11, 311--336.
(CNTP)
8. (with Boris Dubrovin) Generating series for GUE correlators.
Letters in Mathematical Physics, 2017, 107, 1971--2012.
(LMP)
7. (with Marco Bertola and Boris Dubrovin) Simple Lie algebras and topological ODEs.
IMRN, 2018, 2018, 1368-1410.
(IMRN)
6. (with Marco Bertola and Boris Dubrovin) Correlation functions of the KdV hierarchy and applications
to intersection numbers over \M_{g,n}. Physica D: Nonlinear Phenomena, 2016, 327, 30--57. (PDNP)
5. (with Ferenc Balogh) Geometric interpretation of Zhou's explicit formula for the Witten--Kontsevich tau function.
Letters in Mathematical Physics, 2017, 107, 1837--1857.
(LMP)
4. (with Marco Bertola) The partition function of the extended r-reduced Kadomtsev--Petviashvili hierarchy. J. Phys. A: Math. Theor., 2015, 48, 195205.
(JPA)
3. (with Boris Dubrovin, Si-Qi Liu and Youjin Zhang) Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Advances in Mathematics, 2016, 293, 382--435.
(AM)
2. (with Si-Qi Liu and Youjin Zhang) Uniqueness Theorem of W-Constraints for Simple Singularities. Letters in Mathematical Physics, 2013, 103, 1329--1345.
(LMP)
1. (with A.S. Fokas) On a novel class of integrable ODEs related to the Painlev\'e equations.
International Journal of Bifurcation and Chaos, 2012, 22, 1250211.
(IJBC)
Selected ArXiv E-prints
- (with Boris Dubrovin and Don Zagier) Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality.
arXiv:2101.10924.
- (with Boris Dubrovin and Daniele Valeri) Affine Kac--Moody algebras and tau-functions for the Drinfeld--Sokolov hierarchies: The matrix-resolvent method.
arXiv:2110.06655.
- (with Jindong Guo) On the large genus asymptotics of psi-class intersection numbers.
arXiv:2110.06774.
- (with Si-Qi Liu, Youjin Zhang and Jian Zhou) The Virasoro-like Algebra of a Frobenius Manifold.
arXiv:2112.07526.
- (with Qingsheng Zhang) On the Hodge-BGW correspondence.
arXiv:2112.12736.
- (with Mattia Cafasso) Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method.
arXiv:2112.14202.
- (with Chunhui Zhou) Gelfand--Dickey hierarchy, generalized BGW tau-function, and W-constraints.
arXiv:2112.14595.
Workshops, Schools, and Conferences
Past Teachings
科学与社会研讨课 (2019, 2020); Theory of Integrable Systems (可积系统理论, 2020 秋); Complex Analysis (复分析, 2020 春, 2021 春);
Differential Geometry (微分几何, 2019 秋, 2021 秋), lecture notes: part 1 ,
part 2 , part 3 ,
part 4 , part 5 , USTC;
Linear Algebra (线性代数, 2019 春), lecture notes: part a ,
part b , quadratics , USTC;
Modern Mathematical Physics Problems (Introduction to Integrable Systems, 2018 秋), USTC;
Introduction to Integrable Systems (2018 Spring), MPIM;
Frobenius Manifolds, MPIM (2017 Spring); Introduction to Frobenius Manifolds, SISSA (2016 Spring)
Past Seminars, USTC
Past Workshops, Schools, and Conferences
summer school , 2021, USTC, Hefei, P.R. China
Gromov-Witten Invariants and Integrable Systems, workshop and winter school , December 28-31, 2018, USTC, Hefei, P.R. China
Integrability and Randomness in Geometry and Mathematical Physics, conference, April 8-12, 2019, Luminy, France
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