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