Li, Lei

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

Office: 515 Baoyugang Lib
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

Positions

Tenure track Associate Professor, SJTU; 2018-present

Assistant Research Professor, Duke University, 2015-2018

Education

2010-2015. Mathematics. Phd. UW-Madison.
Major: Applied math; Minor: Probability and analysis; Advisor: Saverio Spagnolie

2013. Mathematics. MA. UW-Madison

2012. Computer Science. MS. UW-Madison.

2006-2010. Mathematics and Physics(基科) (applied). BS. Tsinghua University, Beijing.

Preprints

A stochastic version of Stein Variational Gradient Descent for efficient sampling
L. Li, J. Liu, Z. Liu, J. Lu
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Y. Feng, T. Gao, L. Li, J. Liu, Y. Lu
A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
L. Li, J. Liu
Numerical methods for stochastic differential equations based on Gaussian mixture
L. Li, J. Lu, J. Mattingly, L. Wang
Random batch methods (RBM) for interacting particle systems
S. Jin, L. Li, J. Liu
On mean field limit for Brownian particles with Coulomb interaction in 3D
L. Li, J. Liu, P. Yu
Numerical study of ergodicity for the overdamped generalized Langevin equation with fractional noise
D. Fang, L. Li
Large time behaviors of upwind schemes by jump processes
L. Li, J. Liu
On Runge-Kutta methods for the water wave equation and its simplified nonlocal hyperbolic model
L. Li, J. Liu, Z. Liu, Y. Yang, Z. Zhou

Publications

Patched peakon weak solutions of the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu Physica D To appear
On the diffusion approximation of nonconvex stochastic gradient descent
W. Hu, C. J. Li, L. Li, J. Liu Annals of Mathematical Sciences and Applications To appear
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
Some compactness criteria for weak solutions of time fractional PDEs
L. Li, J. Liu SIAM: Math. Anal. 2018. Vol. 50, Issue 4. 3963-3995
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. 2867-2900 pdf file
A dispersive regularization for the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu SIAM J. Math. Anal. 2018. Vol. 50, Issue 3. 2807-2838 pdf file
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
A note on one-dimensional time fractional ODEs
Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
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
p-Euler equations and p-Navier-Stokes equations
L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
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
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2. pdf file
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
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
Analytical solution for laterally loaded long piles based on Fourier-Laplace integral
F. Liang, Y. Li, L. Li, J. Wang. Applied Mathematical Modelling. 2014. Vol. 38. Issue 21 pdf file
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. 935-964 pdf file
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
The sedimentation of flexible filaments
L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie. Journal of fluid mechanics. 2013. Vol 735. 705-736 pdf file

Thesis

Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
2015. UW-Madison.

Teaching

Shanghai Jiao Tong U.

Advanced Computational Methods, Fall, 2018

Duke

UW-Madison