### DIMACS - Graduate Student Combinatorics Seminar

Title: Outer Automorphisms of S_6

Speaker: **Jason Saied**, Rutgers University

Date: Wednesday, October 19, 2016 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

S_6 is the only symmetric group which has outer automorphisms. (Yep, you read that right. What's so special about six?) We'll spend some time looking at the structure of the automorphism group of S_6 and the pretty properties it has. Among other things, we'll construct the outer automorphisms by playing with icosahedra, use those icosahedra to find some pretty weird (and important!) subgroups of S_6, and cook up a surprisingly simple construction of the Sylvester graph. This is based on work I did at Lafayette College with Dantong Zhu.

See: http://www.math.rutgers.edu/~ajr224/GCS.html