Li, Lei

Department of Mathematics,
Duke University

Office: 222 Physics
E-mail: leili AT math DOT duke DOT edu

Here are my CV and research statement.

About

I'm a William W. Elliott Assistant Research Professor at Duke Mathematics Department. My interest lies in applied math, including

Education

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

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
Patched peakon weak solutions of the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu

Publications

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 Communications in Mathematical Sciences To appear
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: 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
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
Continuous and discrete one dimensional autonomous fractional ODEs
Y. Feng, L. Li, J. Liu, X. Xu Discrete and Continuous Dynamical Systems- Series B, In press
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

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

Notes

Notes for my graduate study

Questions in study

Some examples of problems