#### Home>People>Faculty

LIU Xiaobo
Chair Professor
xbliu@math.pku.edu.cn
Phone :86-10-62744137
Office :78202W

### Education

 Ph. D University of Pennsylvania 1994 B. S. Tsinghua University 1987

### Research Interests

Differential Geometry and Mathematical Physics

1. Quantum Cohomology and Gromov-Witten Invariants

2. Moduli spaces of curves

3. Isoparametric submanifolds

4. Volume minimizing cycles in Riemannian manifolds

### Selected Publications

• X. Liu and G. Wang, “Connecting the Kontsevich-Witten and Hodge tau-functions by the $\widehat{GL(\infty)}$ Operators”, Comm. Math. Phys., vol. 346 (2016), pp 143-190.
• X. Liu and X. Wang, “Genus-2 G-functions for $P^1$ orbifolds.” Advances in Mathematics, Vol. 274 (2015), pp 631-650.
• X. Liu and X. Wang, “Conditions for the vanishing of the genus-2 G-function.” Transactions of American Mathematical Society, vol. 367 (2015), pp 8975--8996.
• X. Liu, “Genus-1 Virasoro conjecture along quantum volume direction.” International Mathematical Research Notices, vol. 2013 issue 8 (2013), pp 1747-1760.
• X. Liu and R. Pandharipande, “New topological recursion relations.” Journal of Algebraic Geometry, Vol. 20 (2011), 479--494.