My research interests are in the field of symplectic geometry and symplectic topology including
Gromov-Witten theory, quantum cohomology and Floer homology. In recent years, I have been working on
the foundation of Gromov-Witten type theories.
Publications
Liu, G. Associativity of Quantum Multiplication. Comm Math Phys (1998) 191: 265. https://doi.org/10.1007/s002200050268
Liu, G.; Tian, G. Floer homology and Arnold conjecture. J. Differential Geom. 49 (1998), no. 1, 1--74. doi:10.4310/jdg/1214460936. https://projecteuclid.org/euclid.jdg/1214460936
Liu, G.; Tian, G. On the equivalence of multiplicative structures in floer homology and quantum homology. Acta Math Sinica (1999) 15: 53. https://doi.org/10.1007/s10114-999-0060-x
Liu, G.; Tian, G. Weinstein Conjecture and GW-invariants. Communications in Contemporary MathematicsVol. 02, No. 04, pp. 405-459 (2000) https://doi.org/10.1142/S0219199700000256
Liu, G Moduli Space of Stable Maps. in Mirror Symmetry IV. page 57-77 Edited by D'Hoker, Phong and Yau, 2002.
Recent Pre-prints
Liu, G. On Action of $PSL(n+1, {\bf C})$ on Space of $L_k^p$-maps on ${\bf P}^n$, 2019 (arXiv link), submitted to Pure and Applied Mathematics Quarterly
Liu, G. On Nonlinear Part of Filled-Section in Splicing, 2018 (arXiv link)
Liu, G. On Linear Part of Filled-Section in Splicing, 2018 (arXiv link)
Liu, G. Higher-degree Smoothness of Perturbations III, 2018 (arXiv link)
Liu, G. Higher-degree Smoothness of Perturbations II, 2018 (arXiv link)
Liu, G. Higher-degree Smoothness of Perturbations I, 2017 (arXiv link)
Liu, G. On Stability of Nodal L^p_k-Maps I, 2015 (arXiv link) submitted to Pure and Applied
Mathematics Quarterly
Liu, G. Geometric Equivariant Extension of Sections in GW Theory I, 2015 (arXiv link)
Liu, G. On the Action of Reparametrization Group on the Space of L^p_k-maps I, 2013 (arXiv link)
Liu, G. C^(m_0)-Smoothness of Evaluation Maps, 2013 (arXiv link)
Liu, G. Weakly Smooth Structures in Gromov-Witten Theory, 2013 (arXiv link)