53 citations · 204 across the 31 of their papers we have counts for
7 papers · 1 filter
Complexity of quantum cohomology
Xiaobo Liu, Chongyu Wang
Circuit complexity for two-dimensional topological quantum field theories (2D TQFT) was defined by Couch, Fan, and Shashi in [12]. In this paper, we study complexity for the 2D TQF…
Schur Q-Polynomials and Kontsevich-Witten Tau Function
Xiaobo Liu, Chenglang Yang
Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will…
Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators
Xiaobo Liu, Haijiang Yu
In this paper, we show that the generating function for linear Hodge integrals over moduli spaces of stable maps to a nonsingular projective variety can be connected to the gen…
New topological recursion relations
Xiaobo Liu, Rahul Pandharipande
Simple boundary expressions for the k-th power of the cotangent line class on the moduli space of stable 1-pointed genus g curves are found for k >= 2g. The method is by virtual lo…
Quantum product on the big phase space and the Virasoro conjecture
Xiaobo Liu
We first study the quantum product on the big phase space defined by gravitational Gromov-Witten invariants. We then use this product to give an interpretation for various topologi…
Elliptic Gromov-Witten Invariants And Virasoro Conjecture
Xiaobo Liu
The Virasoro conjecture proposed by Eguchi-Hori-Xiong and S. Katz predicts that the generating function of Gromov-Witten invariants is annihilated by infinitely many differential o…
Virasoro Constraints For Quantum Cohomology
Xiaobo Liu, Gang Tian
Eguchi-Hori-Xiong and S. Katz proposed a conjecture that the partition function of topological sigma model coupled to gravity is annihilated by infinitely many differential operato…