Low-dimensional topology, low-dimensional field theory and representation theory

TL;DR

This paper explores the interplay between low-dimensional topology, geometry, and quantum field theory, illustrating how these areas inform and inspire advances in algebra and representation theory.

Contribution

It provides a personal perspective on how structures from low-dimensional topology and field theory influence algebraic and categorical concepts in representation theory.

Findings

Connections between topology, geometry, and algebra are elucidated.

Field theory ideas inspire new approaches in representation theory.

The paper offers a synthesis of recent interdisciplinary developments.

Abstract

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We present a personal view on some of these instances which have appeared within the Research Priority Programme SPP 1388 ``Representation theory''.