Abstract:

The K(\pi,1)-conjecture for Artin groups, originating in work of Arnol'd, Brieskorn, Pham, and Thom, predicts that a natural complex manifold associated to an Artin group is its classifying space. It is a central problem in the theory of Artin groups, with connections to singularity theory, algebraic geometry, representation theory, and low-dimensional topology.

This minicourse will explain a geometric approach to the conjecture using new forms of non-positive curvature for singular spaces. These methods give a complete solution in dimension 3, as well as large classes of higher-dimensional cases.

We will discuss background on Artin and Coxeter groups, classical and recent notions of non-positive curvature, local-to-global principles, and the resulting curvature hierarchy for Artin groups. The course is based on joint work with Piotr Przytycki and joint work with Nima Hoda.

Lecture 1:  15:00-17:00 June 22, 2026

Lecture 2:  15:00-17:00 June 23, 2026

Lecture 3:  10:00-12:00 June 25, 2026