96 citations · 194 across the 16 of their papers we have counts for
8 papers · 1 filter
Constructing the LG/CY isomorphism between geometries
Huijun Fan, Tian Lan, Zongrui Yang
For a nondegenerate homogeneous polynomial with degree , we can obtain a structure from the Landau-Ginzburg model $(\C^{n+2}, f)$…
LG/CY correspondence between geometries
Huijun Fan, Tian Lan, Zongrui Yang
The concept of geometric structure was introduced by physicists (see \cite{CV1, BCOV} and references therein) , and then studied firstly in mathematics by C. Hertling \cite{…
The Moduli Space in the Gauged Linear Sigma Model
Huijun Fan, Tyler Jarvis, Yongbin Ruan
This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most gener…
A Mathematical Theory of the Gauged Linear Sigma Model
Huijun Fan, Tyler Jarvis, Yongbin Ruan
We construct a mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group.…
Quantum Singularity Theory for A_{r-1} and r-Spin Theory
Huijun Fan, Tyler J. Jarvis, Yongbin Ruan
We give a review of the quantum singularity theory of Fan-Jarvis-Ruan and the r-spin theory of Jarvis-Kimura-Vaintrob and describe the work of Abramovich-Jarvis showing that for th…
Witten's D_4 Integrable Hierarchies Conjecture
Huijun Fan, Amanda Francis, Tyler J. Jarvis +2
We prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D_4 with symmetry group <J> and D_4^T with symmetry group G_{max}, respectively,…
Quantum ring of singularity
Huijun Fan, Yefeng Shen
In this paper, we will prove that the quantum ring of the quasi-homogeneous polynomial with some admissible symmetry group defined by Fan-Jarvis-Ruan…
The Witten equation and its virtual fundamental cycle
Huijun Fan, Tyler J. Jarvis, Yongbin Ruan
We study a system of nonlinear elliptic PDEs associated with a quasi-homogeneous polynomial. These equations were proposed by Witten as the replacement for the Cauchy-Riemann equat…