Department of Mathematics

Krieger School of Arts and Sciences

Johns Hopkins University

3400 N. Charles Street, Baltimore, MD 21218

Office: 311 Krieger Hall

Email: xzheng@math.jhu.edu

Tel: 410-516-0156

I am a J.J. Sylvester Assistant Professor in the Department of Mathematics, Johns Hopkins University. I graduated with my Ph.D. from the University of Illinois at Chicago under Professors Lawrence Ein and Kevin Tucker. Before that, I grew up and studied in China. My undergraduate advisor is Shiu-Chun Wong at Zhejiang University.

** Spring 2019 teaching: **

Math 619, Lie Groups and Lie Algebras

Math 644, Algebraic Geometry II

** Research:**

I am interested in algebraic geometry with two directions. My first line of research focuses on the geometry of the Hilbert scheme of points on singular curves and surfaces. I aim to understand invariants and singularities of these Hilbert schemes of points. I am also interested in various algebro-geometric problems over fields of positive characteristics, specifically linear systems on surfaces.

- Equivariant Hilbert schemes (in preparation).
- The Hilbert schemes of points on surfaces with rational double point singularities (submitted).
- Counterexamples to Kodaira vanishing theorem on surfaces (to appear).
- Ph.D. Thesis.