# Welcome to Lei Zhang's Homepage

I am now a research professor (tenure track) at School of Mathematical Sciences of USTC. Before joining USTC, I was a member of School of Math., Shaanxi Normal University (2011-2018).

I got my Bachelor's degree from Tianjin University (2001-2005) and Ph.D. from Peking University (Supervised by Prof. Jin-Xing Cai, 2005-2011). Here is my CV.

Office: 管理科学楼1531

Email：zhlei18@ustc.edu.cn

## News and Information

Here are some useful Links. For suggestions to graduate students, I agree with and refer to Prof. Liang.

## Teaching

2019 Fall, Basic Algebraic Geometry 1:Varieties in Projective Space(Igor R.Shafarevich)

2019 Sring, Algebraic Geometry and Arithemetic curves(Qing Liu)

2018 Fall, Complex Variable Functions(（复变函数，严镇军 )

2018 Spring, Riemann Surface （黎曼曲面导引，梅加强）

## Research

My research area is Algebraic Geometry, and study topics: Algebraic Surface, Irregular Variety, Minimal Model Theory in positive characteristic. Recently I focus on minimal model theory in characteristic p.

### Accepted papers:

[16] Lei Zhang, Abundance for 3-folds with non-trivial Albanese maps in positive characteristic, to appear in Journal of the European Mathematical Society, arXiv: 1705.00847.

[15] Lei Zhang, Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics, Advances in Mathematics 354, (2019), https://doi.org/10.1016/j.aim.2019.106741.

[14] C.D. Hacon, Z. Patakfalvi and L. Zhang, Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p > 0, Duke Mathematical Journal 168 (9) (2019), 1723--1736.

[13] Chenyang Xu and Lei Zhang, Nonvanishing for threefolds in characteristic p>5, Duke Mathematical Journal, 168 (7) (2019),1269--1301.

[12] Lei Zhang, Abundance for non-uniruled 3-folds with non-trivial Albanese maps in positive characteristics, Journal of London Mathematical Society, 99 (2) (2019), no. 2, 332--348.

[11] Yong Hu and Lei Zhang, Surfaces with p_g = q= 1, K^2 = 6 and non-birational bicanonical maps, Acta Mathematica Sinica (English Series) 35 (3) (2019), 321--337.

[10] Sho Ejiri and Lei Zhang, Iitaka's conjecture for 3-folds in positive characteristic, Mathematical Research Letters 25 (2018), 783--802.

[9] Lei Zhang, A note on Iitaka's conjecture C_{3,1} in positive characteristics, Taiwanese Journal of Mathematics,21 (2017), 689--704.

[8] Caucher Birkar, Yifei Chen and Lei Zhang, Iitaka's C_{n,m} conjecture for 3-folds over finite fields, Nagoya Mathematical Journal 229 (2018), 21--51.

[7] Lei Zhang, Surfaces with p_g=q = 1, K^2 = 7 and nonbirational bicanonical maps, Geometriea Dedicata 177 (2015), 293--306.

[6] Yifei Chen and Lei Zhang, The subadditivity of the Kodaira dimension for fibrations of relative dimension one in positive characteristic, Mathematical Research Letters 22 (2015), 675--696.

[5] Lei Zhang, The cohomological support locus of pluricanonical sheaves and the Iitaka fibration, Journal of London Mathematical Society 90 (2014), 592--608.

[4] Lei Zhang, A note on the linear systems on the projective bundles over abelian varieties, Proceedings of American Mathematical Society 142 (2014), 2569--2580.

[3] Lei Zhang, On the bicanonical map of primitive varieties with q(X) = dim X: the degree and the Euler number, Mathematische Zeitschrift 277 (2014), 575--590.

[2] Jin-xing Cai, Wenfei Liu and Lei Zhang, Automorphisms of surfaces of general type with q\geq 2 acting trivially in cohomology, Compositio Mathematica 149 (2013), 1667--1684.

[1] Lei Zhang, Characterization of a class of surfaces with p_g=0 and K^2 = 5 by their bicanonical maps, Manuscripta Mathematica 135 (2011), 165--181.