Math 415

Math 415 Topics in Algebra: Braid Groups and Mapping Class Groups

Braid groups and mapping class groups are important in the study of both topology and group theory. In this course, we will be looking at them from a more group theoretic point of view. The class will be accessible to first and second year graduate students. For braid groups, we will cover automatic structures, recent linearity results, the conjugacy problem and its connection to cryptography, orderability, and Artin and Garside groups, which are natural generalizations. For mapping class groups, we will look at the Neilsen-Thurston classification of mapping classes, train tracks, continued fractions, and an automatic structure. We will finish by discussing open questions. Students will be asked to give an in-class talk on a current paper.

Recommended textbooks

Survey papers and other interesting links (list still in preparation)