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My research area is Algebraic Geometry, and study topics: Algebraic Surface, Irregular Variety, Minimal Model Theory 

in positive characteristic. Recently my research interest lies in Hodge conjecture and related topics.

Research papers:

[25] Tongji Gao, Zhan Li and Lei Zhang, Varieties with nef anticanonical divisors and Albanese morphisms of relative dimension one in positive characteristic, arXiv:2510.17161v1.

[24] Feng Hao, Zichang Wang and Lei Zhang, Good minimal models with nowhere vanishing holomorphic 1-forms, to appear in Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienz, arXiv: 2412.12582. 

[23] Zichang Wang and Lei Zhang,  An example with non-linear special locus in the space of holomorphic one-forms, to appear in Chinese Annals of Mathematics. Series B.

[22] Jinshan Chen, Chongning Wang and Lei Zhang, On canonical bundle formula for fibrations of curves in positive characteristic, to appear in Forum of Mathematics, Sigma, arXiv: 2308.08927.

[21] Jingshan Chen, Chongning Wang and Lei Zhang, Irregular threefolds with numerically trivial canonical divisor, Nagoya Mathematical Journal (2026), 261:e12 1–37 doi:10.1017/nmj.2025.10093,  arXiv:2409.19973.

[20] Miaomiao Mu and Lei Zhang, On Bogomolov inequality on fibred surfaces in positive characteristic, International Journal of Mathematics 36 (2025), no. 12, Paper No. 2550046, 18 pp.

[19] Lei Zhang,  Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic, Algebra & Number Theory 16 (2022), no. 10, 2339–2384.  arXiv: 2010. 08897.

[18] Yi Gu, Lei Zhang and Yongming Zhang, Counterexamples to Fujita's conjecture on surfaces in positive characteristic,  Advances in Mathematics 400 (2022), Paper No. 108271, 17 pp. arXiv: 2002. 04584.

[17] Paolo Cascini, Sho Ejiri, Janos Kollar and Lei Zhang, Subadditivity of Kodaira dimension does not hold in positive characteristic, Commentarii Mathematici Helvetici 96 (2021), no. 3, 465--481. arXiv: 2003. 13206.

[16] Lei Zhang, Abundance for 3-folds with non-trivial Albanese maps in positive characteristic, Journal of the European Mathematical Society 22 (2020), no. 9, 2777--2820. arXiv: 1705.00847.

[15] Lei Zhang, Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics, Advances in Mathematics 354(2019), Advances in Mathematics, 354 (2019), 106741, 29 pp.

[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 the 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 the 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 the 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>= 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.