Current Topics Seminar

Speaker Erik Slivken
Title The Sandpile Group of Erd\"{o}s R\'{e}nyi Random Graphs
Date April 14 4:00pm PDL C-36
The abelian sandpile model first arose in the analysis of dissipative behavior on a lattice. This model extends to a generic graph $G=(V,E)$ and has a group structure whose order is equal to the number of spanning trees of $G$. In this talk we will define the model and look at some specific examples. Then, shifting our focus in more probabilistic direction, we ask for an Erd\"{o}s-R\'{e}nyi random graph, what is the probability that the sandpile group is cyclic ? Does this probability converge to a limit as $n$ increases? If so, does the limit depend on the edge probability $p$? \\ \noindent This talk will assume no prior knowledge of the subject and is meant to be introduction to a wonderful area of discrete mathematics that pulls from algebra, probability, combinatorics and more!