Fan Yang

Department of Mathematics, UCLA
University of California, Los Angeles
520 Portola Plaza
Los Angeles, CA 90095-1555

Office: MS 3949
E-mail: fyang75@math.ucla.edu
Phone: (608) 358 8891


About me

I am a fifth year graduate Student of Department of Mathematics, UCLA.

I have already got a PhD in Physics at The Chinese University of Hong Kong (2014). My PhD advisor was Prof. Ren-Bao Liu.

I received my Bachelor's degree from Tsinghua University (2009). My undergraduate research advisor was Prof. Ke-Qin Zhu, Professor of Fluid Mechanics.

If you want to learn more about me, this is my CV.


Research Interests

I am interested in probability theory and its applications; mathematical physics; quantum mechanics and condensed matter physics. So far I have done research on:


Publications

Probability and random matrix theory

Edge universality of separable covariance matrices. arXiv:1809.04572 (2018) [preprint].

Random band matrices in the delocalized phase, III: Averaging fluctuations (With Jun Yin). arXiv:1807.02447 (2018) [preprint].

Random band matrices in the delocalized phase, II: Generalized resolvent estimates (With Paul Bourgade, Horng-Tzer Yau and Jun Yin). arXiv:1807.01562 (2018). [preprint].

Convergence of eigenvector empirical spectral distribution of sample covariance matrices (With Haokai Xi and Jun Yin). Under revision Annals of Statistics, arXiv:1705.03954 (2017). [preprint].

The smallest singular value of deformed random rectangular matrices. arXiv:1702.04050 (2017). [preprint].

A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices (With Xiucai Ding). Annals of Applied Probability, Vol. 28 (2018): pp 1679-1738. [link].

Local circular law for the product of a deterministic matrix with a random matrix (With Haokai Xi and Jun Yin). Electronic Journal of Probability, Vol. 22 (2017): paper no. 64, 77pp. [link].

Geometric phases in condensed matter physics

Geometric diffusion of quantum trajectories (With Ren-Bao Liu). Scientific Reports 5, 12109 (2015) [link].

Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators (With Ren-Bao Liu). Phys. Rev. B 90, 245205 (2014) [link].

Giant Faraday rotation induced by the Berry phase in bilayer graphene under strong terahertz fields (With Xiaodong Xu and Ren-Bao Liu). New J. Phys. 16, 043014 (2014) [link].

Terahertz electron-Hole recollisions in GaAs/AlGaAs quantum wells: robustness to scattering by optical phonons and thermal fluctuations (With H. Banks, B. Zaks, S. Mack, A. C. Gossard, R. Liu and M. S. Sherwin). Phys. Rev. Lett. 111, 267402 (2013) [link].

Berry phases of quantum trajectories of optically excited electron-hole pairs in semiconductors under strong terahertz fields (With Ren-Bao Liu). New J. Phys., Vol. 15, 115005 (2013) [link].

Non-Newtonian Fluid dynamics

A note on the definition of fractional derivatives applied in rheology (With Ke-Qin Zhu). Acta Mech. Sin., Vol. 27, 866-876 (2011) [link].

On the definition of fractional derivatives in rheology (With Ke-Qin Zhu). Theor. Appl. Mech. Lett., Vol. 1, 012007 (2011) [link].

Can we obtain a fractional Lorenz system from a physical problem (With Ke-Qin Zhu). Chin. Phys. Lett., Vol. 27, 124701 (2010) [link].

Generalized Lorenz equation derived from thermal convection of viscoelastic fluids in a loop (With Ke-Qin Zhu). Chin. Phys. Lett., Vol. 27, 034601 (2010) [link].


Teaching

2018 Fall, MATH 170A: Probability Theory, (Teaching assistant)

2018 Fall, MATH 275A: Probability Theory (for graduate), (Teaching assistant)

2018 Spring, MATH 170E: Introduction to Probability and Statistics, (Teaching assistant)

2018 Winter, MATH 32A: Calculus of Several Variables, (Teaching assistant)

2017 Fall, MATH 31A: Differential and Integral Calculus, (Teaching assistant)