An ICERM semester-long program is being organized by Prof. John Etnyre and others, which will focus on braid groups, mapping class groups, and their generalizations.

Abstract

Braid groups were introduced by Emil Artin almost a century ago. Since then, braid groups, mapping class groups, and their generalizations have come to occupy a significant place in parts of both pure and applied mathematics. In the last 15 years, fields with an interest in braids have independently undergone rapid development; these fields include representation theory, low-dimensional topology, complex and symplectic geometry, and geometric group theory. Braid and mapping class groups are prominent players in current mathematics not only because these groups are rich objects of study in their own right, but also because they provide organizing structures for a variety of different areas. For example, in modern representation theory, important equivalences of categories are organized into 2-representations of braid groups, and these same 2-representations appear prominently in parts of geometry and mathematical physics concerned with mirror dualities; in low-dimensional topology, manifolds are presented and related to each other via braids and mapping classes.

Computational applications and questions about braid groups have also emerged in disparate mathematical contexts; in some cases, these coalesce around the same computational problem. For example, developing fast machine-based calculations of link homology invariants is a goal shared by representation theorists, low-dimensional topologists, symplectic and algebraic geometers, and string theorists. The proposed semester program aims to bring together researchers working in diverse areas through the common thread of their interaction with braid and mapping class groups. The overarching goals of the program are to establish and clarify the key questions driving each field, and to improve each group’s understanding of the tools, techniques, and perspectives of the others.

Organizing Committee

• Marc Culler
  University of Illinois at Chicago
• Ben Elias
  University of Oregon
• John Etnyre
  Georgia Institute of Technology
• Benson Farb
  University of Chicago
• Juan González-Meneses
  Universidad de Sevilla
• Matthew Hedden
  Michigan State University
• Keiko Kawamuro
  University of Iowa
• Anthony Licata
  Australian National University
• Joan Licata
  Australian National University

Confirmed Speakers & Participants

See the ICERM website 

https://icerm.brown.edu/programs/sp-s22/