Topology Seminar (Introductory Talk): From random graphs to random groups

Seminar | October 14 | 2:10-3 p.m. | 740 Evans Hall

 Moon Duchin, Tufts University

 Department of Mathematics

The study of random graphs took off in the mid-twentieth century and became a rich and beautiful research area. A few decades later, people exported that success to the study of groups. I'll introduce the field of random groups from scratch and survey some of the interesting results. The main idea is that you start with an alphabet of generators and then add relators as random strings in that alphabet. You get surprisingly good control on the algebra and geometry of the resulting group as you vary the density of the relators.