Description: The main aim of geometric group theory is to understand an infinite group by studying geometric objects on which the group acts. This fascinating subject ties together areas of geometry/topology, probability theory, complex analysis, combinatorics and representation theory. Depending on specific interests, we can read any one of the following texts, or jump around between them:
(1) “Primer on mapping class groups”, by Farb and Margalit: a study of the mapping class group of a surface, one of the most fundamentally important groups in low-dimensional topology.
(2) “Notes on notes of Thurston”, by Canary, Epstein & Marden: a summarized version of Thurston’s famous “notes” on hyperbolic geometry and 3-manifolds.
(3) “Trees”, by Serre, and “Topological methods in group theory”, by Scott and Wall: these readings summarize tools used to study groups which act on contractible graphs.
Term:
Spring
Prerequisites:
basics of algebraic topology (fundamental group, quotient spaces).
Year:
2015