TCC Course: Abelian Sandpiles and related topics
Lecturer contact information: Email: A.Jarai@bath.ac.uk
Phone: (01225) 384264
This course is about an intriguing model in probability that has deep
connections to various fields of mathematics and physics:
random walk and potential theory;
spanning trees and the Tutte polynomial in combinatorics;
critical phenomena in statistical physics and conformal field theory;
Abelian groups in algebra.
The model is very easy to define (in fact can be explained to non-mathematicians),
yet many fundamental questions about it turn out to be interesting and hard.
For an appetizer, see the short
article by Levine and Propp.
Pre-requisites: undergraduate mathematics and a familiarity with
Lectures are on Mondays 9:15-11:15, starting 8 October 2018,
for 8 weeks. The Bath lectures will be in the room 3W 4.13.
Other venues TBA.
The lectures are broadly based around
my survey paper,
with some additional material.
Lecture notes:Lecture 8 October: handwritten, board
Lecture 15 October: handwritten, board
Lecture 22 October: handwritten, board
Lecture 29 October: handwritten, board
Lecture 5 November: handwritten, board
Lecture 12 November: handwritten
Lecture 19 November: handwritten, board
Lecture 26 November: handwritten, board
Levine and Propp's paper
Wesley Pegden's sandpile gallery
Burning bijection illustration
Levine's simulation of rotor-router aggregation
Levine and Peres' paper