Li, Lei

Institute of Natural Sciences; School of mathematical sciences.
Shanghai Jiao Tong University

Office: 323 Science Building No. 5
E-mail: leili2010 AT sjtu DOT edu DOT cn

Here is my CV.

About

I'm a tenure track Associate Professor at Shanghai Jiao Tong University. My interest lies in applied math, including

• Computational Math (random algorithms, numerical SDEs and PDEs)
• Analysis of differential equations (PDE models, optimal transport etc, time fractional differential equations)
• Fluid-Structure interaction

Positions

Tenure track Associate Professor, SJTU; 2018-present

Assistant Research Professor, Duke University, 2015-2018

Education

2010-2015. Mathematics. Phd. UW-Madison.

2013. Mathematics. MA. UW-Madison

2012. Computer Science. MS. UW-Madison.

2006-2010. Mathematics and Physics. BS. Tsinghua University, Beijing.

Preprints

Publications

1. Complete Monotonicity-preserving numerical methods for time fractional ODEs
   L. Li, D. Wang Comm. Math. Sci. Accepted
2. Convergence of Random Batch Method for interacting particles with disparate species and weights
   S. Jin, L. Li, J. Liu SIAM J. Numer. Anal. Accepted
3. On the mean field limit of Random Batch Method for interacting particle systems
   S. Jin, L. Li Science China Mathematics Accepted
4. A consensus-based global optimization method for high dimensional machine learning problems
   J. A. Carrillo, S. Jin, L. Li, Y. Zhu ESAIM: Control, Optimisation and Calculus of Variations Accepted
5. Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on R by jump processes
   L. Li, J. Liu Math. Comp. 2020. Vol. 89, No. 235, 2283--2320 pdf file
6. A stochastic version of Stein Variational Gradient Descent for efficient sampling
   L. Li, Y. Li, J. Liu, Z. Liu, J. Lu Commun. Appl. Math. Comput. Sci.(CAMCoS) 2020. Vol. 15, Issue 1, 37--63
7. A random-batch Monte Carlo method for many-body systems with singular kernels
   L. Li, Z. Xu, Y. Zhao SIAM J. Sci. Comput. 2020. Vol. 42, No. 3, A1486-A1509 pdf file
8. Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
   Y. Feng, T. Gao, L. Li, J. Liu, Y. Lu Comm. Math. Sci. 2020. Vol. 18, Issue 1 pdf file
9. Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise
   D. Fang, L. Li ESAIM: Math. Model. Numer. Anal. 2020. Vol. 54, No. 2, 431-463 pdf file
10. On the mean field limit for Brownian particles with Coulomb interaction in 3D
    L. Li, J. Liu, P. Yu J. Math. Phys. 2019. Vol. 60. 111501 pdf file
11. Random batch methods (RBM) for interacting particle systems
    S. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
12. A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
    L. Li, J. Liu SIAM J. Numer. Anal. 2019. Vol. 57, No. 5, 2095-2120 pdf file
13. Patched peakon weak solutions of the modified Camassa-Holm equation
    Y. Gao, L. Li, J. Liu Physica D: Nonlinear Phenomena 2019. Vol. 390. 15-35 pdf file
14. On the diffusion approximation of nonconvex stochastic gradient descent
    W. Hu, C. J. Li, L. Li, J. Liu Annals of Mathematical Sciences and Applications 2019. Vol. 4, No. 1, 3-32 pdf file
15. Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
    Y. Feng, L. Li, J. Liu Comm. Math. Sci. 2018. Vol. 16, No. 3 pdf file
16. Some compactness criteria for weak solutions of time fractional PDEs
    L. Li, J. Liu SIAM: Math. Anal. 2018. Vol. 50, Issue 4. 3963-3995 pdf file
17. A generalized definition of Caputo derivatives and its application to fractional ODEs
    L. Li, J. Liu SIAM: J. Math. Anal. 2018. Vol. 50, Issue 3. 2867-2900pdf file
18. A dispersive regularization for the modified Camassa-Holm equation
    Y. Gao, L. Li, J. Liu SIAM J. Math. Anal. 2018. Vol. 50, Issue 3. 2807-2838pdf file
19. Cauchy problems for Keller-Segel type time-space fractional diffusion equation
    L. Li, J. Liu, L. Wang J. Differ. Equations 2018. Vol. 265, Issue 3 pdf file
20. A note on one-dimensional time fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
21. Continuous and discrete one dimensional autonomous fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Discrete and Continuous Dynamical Systems- Series B 2018. Vol. 23, Issue 8 pdf file
22. p-Euler equations and p-Navier-Stokes equations
    L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
23. A note on deconvolution with completely monotone sequences and discrete fractional calculus
    L. Li, J. Liu Quart. Appl. Math. 2018. Vol. 76, Issue 1 pdf file
24. Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
    L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
25. A locally gradient preserving reinitialization for level set functions
    L. Li, X. Xu, S. E. Spagnolie Journal of Scientific Computing. 2017. Vol. 71, Issue 1. pdf file
26. Swimming and pumping by helical waves in viscous and viscoelastic fluids
    L. Li, S. E. Spagnolie Physics of fluids. 2015. Vol. 27, Issue 2.pdf file
27. Analytical solution for laterally loaded long piles basedon Fourier-Laplace integral
    F. Liang, Y. Li, L. Li, J. Wang. Applied Mathematical Modelling. 2014. Vol. 38. Issue 21 pdf file
28. The instability of a sedimenting suspension of weakly flexible fibres
    H. Manikantan, L. Li, S. E. Spagnolie, D. Saintillan. Journal of fluid mechanics. 2014. Vol 756. 935-964pdf file
29. Swimming and pumping of rigid helical bodies in viscous fluids
    L. Li, S. E. Spagnolie, Physics of fluids. 2014. Vol. 26, Issue 4.pdf file
30. The sedimentation of flexible filaments
    L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie. Journal of fluid mechanics. 2013. Vol 735. 705-736pdf file

Thesis