SS5 Algorithmic and Combinatorial Group Theory

Algorithmic and combinatorial group theory explores groups through presentations by generators and relations, focusing on the algorithmic questions that emerge from these descriptions.

Fundamental challenges, such as the word, isomorphism, and conjugacy problems, motivate much of the research in this field and have led to the development of diverse combinatorial and geometric techniques. These ideas play a central role in the study of Artin and braid groups, naturally intersecting with geometric group theory, low-dimensional topology, and computational algebra.

This session will focus on:
• Algorithmic questions in Artin groups, braid groups, and related families;
• Combinatorial and geometric methods for studying group presentations;
• Structural properties of groups exhibiting forms of non-positive or negative curvature;
• Interactions between group theory, topology, and computation.

The proposed speakers conduct research in several closely related directions. Maria Cumplido has developed combinatorial approaches to braid and Artin groups, often utilizing geometric properties derived from their actions on complexes. Bruno Cisneros de la Cruz investigates problems in geometric and combinatorial group theory with significant connections to topology. Davide Spriano examines groups from a geometric perspective, particularly those with negative curvature and the resulting algorithmic questions. Recent work by Oli Jones and Giovanni Sartori explores structural decompositions and rigidity phenomena in Artin groups, specifically as they relate to the isomorphism problem. Federica Gavazzi has researched the structural aspects of Artin-type groups, including virtual Artin groups and related constructions.