### TCC Course: Abelian Sandpiles and related topics

**Lecturer contact information:**

Email: A.Jarai@bath.ac.uk
Phone: (01225) 384264
**Introduction:**
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
measure-theoretic probability.
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
**Pictures:**

Levine and Propp's paper

Wesley Pegden's sandpile gallery

Burning bijection illustration

Levine's simulation of rotor-router aggregation

Levine and Peres' paper