Abelianisation of Connections, Quantum Curves, and Spectral Clusters

Información del proyecto

AbQuantumSpec

Identificador del acuerdo de subvención: 101026083

DOI

10.3030/101026083

Proyecto cerrado

Fecha de la firma de la CE 18 Marzo 2021

Fecha de inicio 1 Septiembre 2022

Fecha de finalización 31 Agosto 2024

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 224 933,76

Aportación de la UE

€ 224 933,76

Coordinado por

THE UNIVERSITY OF BIRMINGHAM
United Kingdom

Periodic Reporting for period 1 - AbQuantumSpec (Abelianisation of Connections, Quantum Curves, and Spectral Clusters)

Período documentado: 2022-09-01 hasta 2024-08-31

Resumen del contexto y de los objetivos generales del proyecto

The project focused on developing the theory of abelianisation of meromorphic connections. Meromorphic connections are a vast geometric generalisation of ordinary differential equations (ODEs) that encompasses many classical, widely studied, and very important equations in mathematical physics. Meromorphic connections encode highly transcendental analytic information which is often difficult to describe using existing mathematical frameworks. The project addressed the challenge of finding a geometric approach to systematically represent and study this data using the geometry of algebraic curves.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

Major obstacles were encountered in the development of the relation of this theory with the exact WKB method. To overcome the challenges, several major old conjectures in the WKB method and exact perturbation theory were proved. These newly established theorems provide a bridge between the abelianisation of meromorphic connections and the semi-classical approximation in quantum theory.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

In addition to the primary objectives, the project laid the foundations of a new geometric theory of resurgence and exact WKB method in quantum mechanics.