# Equivariant Landau--Ginzburg mirror symmetry

## TL;DR

This paper presents a new proof for computing Hodge integrals in FJRW theory using localization, and introduces the first equivariant mirror symmetry framework without concavity, applicable to GLSM studies.

## Contribution

It provides a novel localization-based proof and establishes the first equivariant mirror symmetry without concavity for Landau-Ginzburg models.

## Key findings

- New proof of Hodge integral computations in FJRW theory
- First equivariant mirror symmetry framework without concavity
- Framework suitable for future GLSM research

## Abstract

We give a new proof of the computation of Hodge integrals we have previously obtained for the quantum singularity (FJRW) theory of chain polynomials. It uses the classical localization formula of Atiyah--Bott and we phrase our proof in a general framework that is suitable for future studies of gauged linear sigma models (GLSM). As a by-product, we obtain the first equivariant version of mirror symmetry without concavity, generalizing the work of Chiodo--Iritani--Ruan on the Landau--Ginzburg side.