Abelianisation of Connections, Quantum Curves, and Spectral Clusters

Informazioni relative al progetto

AbQuantumSpec

ID dell’accordo di sovvenzione: 101026083

DOI

10.3030/101026083

Progetto chiuso

Data della firma CE 18 Marzo 2021

Data di avvio 1 Settembre 2022

Data di completamento 31 Agosto 2024

Finanziato da

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Costo totale

€ 224 933,76

Contributo UE

€ 224 933,76

Coordinato da

THE UNIVERSITY OF BIRMINGHAM
United Kingdom

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

Periodo di rendicontazione: 2022-09-01 al 2024-08-31

Sintesi del contesto e degli obiettivi generali del progetto

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.

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

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.

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

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.