Work

Asymptotic Geometry of Non-Abelian Hodge Theory and Riemann–Hilbert Correspondence, Rank Three $$\widetilde{E}_6$$ Case

Year: 2026

Type: article

Abstract: We prove the Geometric P=W conjecture in rank 3 on the three-punctured sphere. We describe the topology at infinity of the related character variety. We use asymptotic abelianization of harmonic bundles away from the ramification divisor and an equivariant approach near the branch points to find the WKB (also known as Liouville–Green or phase-integral) expansion of the involved maps. We analyze the Stokes phenomenon governing their behavior.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-026-02385-1

Authors: Miklós Eper, Szilárd Szabó

Institutions: Budapest University of Technology and Economics, Eötvös Loránd University, HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Budapesti Műszaki és Gazdaságtudományi Egyetem, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap, National Research, Development and Innovation Office