University of Science and Technology of China, Bachelor, 2002-2006

Johns Hopkins University, Master, 2006-2009

Northwestern University, Ph. D (advisor: S. Zelditch), 2009-2012

McGill University, postdoc, 2012-2013

Maryland University College Park, Brin
postdoc, 2013-2015

BICMR, Peking University, assistant professor, 2015-

**Recent research**

For the last two
years, I am interested in the following three topics,

1.
**SYK model**:

With Gang Tian and Dongyi Wei, we
have three papers on the global distribution of eigenvalues of SYK model such
as the global density of eigenvalues, the central limit theorem and the concentration
of measure theorem. The SYK model a random matrix model which is a simple model
of the black hole and it's very topical in physics recently, and it's also a
quantum spin glass model. There are still many interesting open problems in
this new emerging area, such as the behaviors of partition function (recall the
Parisi formula in the spin glass) and the largest
eigenvalue.

2.
**Extreme spacing**:

With D. Wei, we study the small gaps for the circular beta-ensemble and large gaps for CUE and GUE, in all cases, we derived the rescaling limits of extreme gaps based on the proof that the extreme gaps are asymptotic to the Poisson distribution after rescaling.

3.
**Random waves**:

With R. Adler, we get an explicit formula for the supremum of random spherical harmonics by Weyl's tube formula, where we proved that unexpectedly there is a lower bound of critical radius of the embedding/immersion of the sphere to higher dimensional sphere by the spherical harmonics, although the image become more and more twisted.

**Random matrices**

1.Large
gaps of CUE and GUE (with D. Wei)

2.Small gaps
of circular beta-ensemble(with D. Wei)

3.Spectrum of SYK model (with G. Tian and
D. Wei)

4.Spectrum of SYK model II: Central limit
theorem (with G. Tian and D. Wei)

5.Spectrum of
SYK model III: Large deviations and concentration of measures (with G. Tian and D.
Wei)

**Random
geometry**

1.Critical radius and supremum of random spherical harmonics (with R.
Adler), to appear in* Annals of Probability. *

2.Critical radius and supremum of random
spherical harmonics II (with X. Xu and R.
Adler), * **Electronic
Communications in Probability, *Volume 23 (2018), paper no. 50, 11 pp.* *

3.Large deviations for zeros of P(\phi)_2 _{ }random polynomials (with S. Zelditch), *J. Stat. Phys *(2011)
143: 619-635.

4.Critical values of random analytic functions on complex
manifolds

(with S. Zelditch), *Indiana Univ. Math. J.*63.
(2014). no.3.,651-686.

5.Median and mean of the Supremum of L^2^{ }normalized random

holomorphic fields (withS. Zelditch), *J. Funct. Anal. *266 (2014), no. 8, 5085-5107.

6.Random Riesz energies on compact Kahler manifolds (with S.

Zelditch), *Trans. Amer. Math. Soc.*, Vol 365, no. 10, 5579-5604, (2013).

7.Critical values of Gaussian SU(2) random polynomials (with Z.

Wang), *Proceeding
of AMS*, Vol 144, no 2, 2016, 487-502.

8.Correlations
between zeros and critical points of random analytic

functions,
arXiv:1604.07693, to appear in *Trans. Amer. Math. Soc.*

9.Conditional expectations of random holomorphic fields on
Riemann surfaces, *IMRN, *Volume 2017, Issue 14, 4406-4434.

**Geometric analysis and PDEs**

1.Periodic solutions of Abreu's equation (with G. Szekelyhidi), *Math. Res. Lett.*
18 (2011), no. 6, 1271-1279.

2.The global convergence of the Calabi flow on Abelian
varieties

(with H. Huang),*
J. Funct. Anal.* 263 (2012), no. 4, 1129-1146.

3.Bergman metrics and geodesics in the
space of Kahler metrics on

principally polarized Abelian varieties, *Journal
of the Institute of Mathematics of Jussieu *(2012) Volume 11, Issue 01, 1-25.

4.Szasz analytic functions and noncompact Kahler toric
manifolds,

*Journal of Geometric Analysis* (2012), Volume 22,
Number 1, 107-131.

Email: renjie@math.pku.edu.cn