# The random graph and its automorphisms

Boise Algebra, Geometry, and Combinatorics Seminar, Boise, October 2012

*Abstract*: The random graph $\Gamma$ can be characterized as follows: If you were to draw infinitely many dots, and flip a coin to decide whether to draw a line connecting each pair of dots, you’ll probably get $\Gamma$. In this talk we’ll study automorphisms of the random graph, and show that they are as many and varied as graphs themselves.