Mathematics Department

University of Pittsburgh

301 Thackeray Hall, Pittsburgh, PA 15260

Office | 402 Thackeray Hall |

haoxu at pitt .edu |

- Spring 2015: Analytic Geometry and Calculus 2
- Spring 2015: Advanced Calculus 2
- Fall 2014: Advanced Calculus 1
- Spring 2014: Topology 2
- Fall 2013: Analytic Geometry and Calculus 2

- Moduli Spaces of Curves
- Complex Geometry
- Deformation Quantization

- (with Kefeng Liu and Ravi Vakil)
*Formal pseudodifferential operators and Witten's r-spin numbers*, J. Reine. Angew. Math. (to appear). - (with Miroslav Englis)
*Forelli-Rudin construction and asymptotic expansion of Szego kernel on Reinhardt domains*, Osaka J. Math. (to appear). - (with Xiao Chang and Shing-Tung Yau)
*Spanning trees and random walks on weighted graphs*, Pacific J. Math.**273**(2015), 241--255. *Bergman kernel, deformation quantization and Feynman diagram formulas*, Proceedings of Sixth ICCM, Taipei, 2013.- (with Kefeng Liu)
*A remark on Mirzakhani's asymptotic formulae*, Asian J. Math.**18**(2014), 29--52. *Weyl invariant polynomial and deformation quantization on Kahler manifolds*, J. Geom. Phys.**76**(2014), 124--135.- (with Shing-Tung Yau)
*An explicit formula of hitting times for random walks on graphs*, Pure Appl. Math. Q.**10**(2014), 567--581. - (with Shing-Tung Yau)
*Trees and tensors on Kahler manifolds*, Ann. Global Anal. Geom.**44**(2013), 151--168. *Bergman kernel and Kahler tensor calculus*, Pure Appl. Math. Q.**9**(2013), 507--546.*On a graph theoretic formula of Gammelgaard for Berezin-Toeplitz quantization*, Lett. Math. Phys.**103**(2013), 145--169.- (with Shing-Tung Yau)
*Discrete Green's functions and random walks on graphs*, J. Combin. Theory Ser. A,**120**(2013), 483--499. - (with Shing-Tung Yau)
*Nodal domain and eigenvalue multiplicity of graphs*, J. Comb.**3**(2012), 609--622. *A closed formula for the asymptotic expansion of the Bergman kernel*, Comm. Math. Phys.**314**(2012), 555--585.*An explicit formula for the Berezin star product*, Lett. Math. Phys.**101**(2012), 239--264.- (with Kefeng Liu)
*Computing top intersections in the tautological ring of Mg*, Math. Z.**270**(2012), 819--837. - (with Kefeng Liu)
*The n-point functions for intersection numbers on moduli spaces of curves*, Adv. Theor. Math. Phys.**15**(2011), 1201--1236. - (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)
*Mirzakhani'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. Lett.**14**(2007), 1041--1054.

- Geometry and Topology of Manifolds, CMS at Zhejiang University, December 24--26, 2014, Hangzhou.
- OIST Mini Symposium: Moduli Space, Conformal Field Theory and Matrix Models, OIST, March 16--18, 2015, Okinawa.
- Large N limit problems in Kahler Geometry, Simons Center for Geometry and Physics, April 20--June 19, 2015, Stony Brook.
- Workshop on Mathematical Physics and Number Theory, MSC at Tsinghua University, July 22--30, 2014, Beijing.
- 6th International Congress of Chinese Mathematicians (ICCM), National Taiwan University, July 14--19, 2013, Taipei.
- Workshop on Mathematics of String theory, CMS at Zhejiang University, June 30--July 2, 2013, Hangzhou.
- Recent progress on moduli spaces and special varieties, Tsinghua Sanya International Mathematics Forum, December 19--21, 2011, Sanya.
- New Recursion Formulae and Integrablity for Calabi-Yau Spaces, Banff International Research Station, October 16--21, 2011, Banff.
- Riemann Surfaces, Harmonic Maps and Visualization, Osaka City University, December 15--20, 2008, Osaka.
- Geometry of Teichmuller spaces and moduli spaces of curves, CMS at Zhejiang University, July 14--20, 2008, Hangzhou.
- First Geometry Conference of 4 Cities, Morningside Center of Mathematics, June 23--25, 2008, Beijing.
- Hangzhou Conference on Geometric Analysis, CMS at Zhejiang University, December 20--22, 2006, Hangzhou.