## Fan Yang
Department of Mathematics, UCLA |

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:

- Random matrix theory and its application to Statistics
- Random band matrix and Anderson model
- Spin systems and functional inequalities
- Geometric phases in condensed matter physics
- Non-Newtonian Fluid dynamics

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). Journal of Statistical Physics (2019). [link].

Convergence of eigenvector empirical spectral distribution of sample covariance matrices (With Haokai Xi and Jun Yin). To appear 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)