Hao Xu

I am a Postdoc at
Harvard Mathematics Department
One Oxford Street Cambridge MA 02138

Office	Science Center 516
E-Mail	haoxu at math .harvard .edu

Teaching

Fall 2012: Introduction to Algebraic Geometry I
Spring 2012: The Kahler-Einstein Metrics
Fall 2011: Differential Geometry
Spring 2011: Introduction to Algebraic Geometry II
Spring 2010: Integrable Systems and Algebraic Geometry

Research

Algebraic Geometry, Moduli Spaces of Curves
Differential Geometry, Deformation Quantization
Several Complex Variables, Fefferman's Program
Spectral Graph Theory

Papers

An explicit formula for the Berezin star product, Lett. Math. Phys. (to appear).
A closed formula for the asymptotic expansion of the Bergman kernel, Comm. Math. Phys. (to appear).
(with Kefeng Liu), Computing top intersections in the tautological ring of Mg, Math. Z. 270 (2012), 819--837.
(with Kefeng Liu), Descendent integrals and tautological rings of moduli spaces of curves, Geometry and Analysis Vol. 2, Adv. Lect. Math (ALM) 18, (2010), 137--172.
(with Kefeng Liu), A proof of the Faber intersection number conjecture, J. Differential Geom. 83 (2009), 313--335.
(with Kefeng Liu), Mirzakharni's recursion formula is equivalent to the Witten- Kontsevich theorem, Asterisque, 328 (2009), 223--235.
(with Kefeng Liu), Recursion formulae of higher Weil-Petersson volumes, Int. Math. Res. Notices 5 (2009), 835--859.
(with Kefeng Liu), Intersection numbers and automorphisms of stable curves, Michigan Math. J. 58 (2009), 385--400.
(with Kefeng Liu), New results of intersection numbers on moduli spaces of curves, Proc.Nat.Acad.Sci. 104 (2007), 13896--13900.
(with Kefeng Liu), New properties of intersection numbers on moduli spaces of curves, Math. Res. Letter 14 (2007), 1041--1054.

Preprints

On a formula of Gammelgaard for Berezin-Toeplitz quantization, arXiv:1204.2259.
(with Kefeng Liu, Ravi Vakil), Formal pseudodifferential operators and Witten's r-spin numbers, arXiv:1112.4601.
(with Kefeng Liu), A remark on Mirzakhani's asymptotic formulae, arXiv:1103.5136.
(with Kefeng Liu), An effective recursion formula for computing intersection numbers, arXiv:0710.5322.
(with Kefeng Liu), The n-point functions for intersection numbers on moduli spaces of curves, arXiv:math/0701319.