On geometric models in representation theory

Abstract

Geometric models have emerged as an important tool in the representation theory of algebras. Surface models associated to gentle algebras have been particularly fruitful in advancing our understanding of their module and derived categories. We give an overview of some of the theoretical advances that geometric surface models for the derived categories of graded gentle algebras and their connections to Fukaya categories of surfaces have made possible.

Proceedings of the ICM 2026, more references in the arXiv version