# About

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

- Analysis of differential equations (PDE models, optimal transport etc, time fractional differential equations)
- Numerical SDEs and PDEs
- 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.

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 appearOn the diffusion approximation of nonconvex stochastic gradient descent

W. Hu, C. J. Li, L. Li, J. Liu

*Annals of Mathematical Sciences and Applications*To appearSemi-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. 3Some compactness criteria for weak solutions of time fractional PDEs

L. Li, J. Liu

*SIAM: Math. Anal.*2018. Vol. 50, Issue 4. 3963-3995A 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 fileA 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 fileCauchy 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 fileA note on one-dimensional time fractional ODEs

Y. Feng, L. Li, J. Liu, X. Xu

*Applied Mathematics Letters*2018. Vol. 83. pdf fileContinuous 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 8p-Euler equations and p-Navier-Stokes equations

L. Li, J. Liu

*J. Differ. Equations*2018. Volume 264, Issue 7 pdf fileA note on deconvolution with completely monotone sequences and discrete fractional calculus

L. Li, J. Liu

*Quart. Appl. Math.*2018. Vol. 76, Issue 1 pdf fileFractional stochastic differential equations satisfying fluctuation-dissipation theorem

L. Li, J. Liu, J. Lu

*J. Stat. Phys.*2017. Vol. 169, Issue 2. pdf fileA 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 fileSwimming and pumping by helical waves in viscous and viscoelastic fluids

L. Li, S. E. Spagnolie

*Physics of fluids.*2015. Vol. 27, Issue 2. pdf fileAnalytical 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 fileThe 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 fileSwimming and pumping of rigid helical bodies in viscous fluids

L. Li, S. E. Spagnolie,

*Physics of fluids.*2014. Vol. 26, Issue 4. pdf fileThe 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

- MATH 660 -Intro. Numer. PDEs, Spring, 2018
- MATH 212 -Multivariable Calculus, Fall, 2017
- MATH 575 -Mathematical Fluid dynamics, Spring, 2017
- MATH 212 -Multivariable Calculus, Fall, 2016
- MATH 660 -Intro. Numer. PDEs, Spring, 2016
- MATH 212 -Multivariable Calculus, Spring, 2016
- MATH 212 -Multivariable Calculus, Fall, 2015

## UW-Madison

- MATH 319 -Differential Equations, Spring, 2015
- MATH 234 -Calculus, Fall, 2014
- MATH 320 -Linear algebra and differential equations
- MATH 234 -Calculus, Fall, 2013
- MATH 340 -Elem Matrix&Linear Algebra, Spring, 2013
- MATH 321 - Applied Mathematical Analysis, Fall, 2012
- MATH 321 - Applied Mathematical Analysis, Spring, 2012
- MATH 222 - Calculus and Analytic Geometry, Fall, 2011
- MATH 222 - Calculus and Analytic Geometry, Spring, 2011
- MATH 222 - Calculus and Analytic Geometry, Fall, 2010