Xiao Jian

Associate Professor

Yau Mathematical Science Center, Tsinghua University

Office: Jing Zhai 202


Personal web page

About me

I am an Associate Professor in YMSC and the math department at Tsinghua University. Before that, I was a Boas Assistant Professor at Northwestern University. I got my PhD in mathematics in 2016, from Université Grenoble Alpes/Fudan University, under the supervision of Professor Jean-Pierre Demailly and Professor Jixiang Fu.


Research areas: complex geometry, complex analytic and algebraic geometry, Kähler geometry, and the interactions with other areas.

Some specific topics: Kähler manifolds, projective manifolds, currents, algebraic/analytic cycles, pluripotential theory, positivity in algebraic/analytic geometry, analytic methods, convexity, Brunn-Minkowski theory, log-concavity, etc.

Below are some recent papers reflecting my interests:

[1] Positivity of valuations on convex bodies and invariant valuations by linear actions (with N.-B. Dang). J. Geom. Anal. 31 (2021), 10718–10777.

[2] Hodge-index type inequalities, hyperbolic polynomials, and complex Hessian equations. Int. Math. Res. Not. IMRN (2021), no.15, 11652–11669.

[3] Positivity functions for curves on algebraic varieties (with B. Lehmann). Algebra & Number Theory 13 (2019), no.6, 1243–1279.

[4] Teissier's problem on the proportionality of big and nef classes over a compact Kähler manifold (with J. Fu). Algebraic Geometry. 6 (2019), no.2, 177–185.

[5] Characterizing volume via cone duality. Math. Ann. 369 (2017), no.3-4, 1527–1555.

[6] Convexity and Zariski decomposition structure (with B. Lehmann). GAFA 26 (2016), no.4, 1135–1189.

For the list of published research papers, see MathSciNet.


In recent years, I teach courses: complex analysis, complex geometry, analytic methods in algebraic geometry, etc.

*Last updated: March 2022