# 18.177 Probability and Random Variables: Fall, 2011

Lectures: Tuesday and Thursday 2:30-4, 2-131

Office hours: After class on Tuesday and
Thursday.

Course announcement and overview

SCHEDULE

Lecture 1 (September 8): Percolation
introduction. Recall
Kolmogorov's zero-one
law
.
Lecture 2 (September 13): Percolation
Lecture 3 (September 15): Percolation
Lecture 4 (September 20): Percolation
Lecture 5 (September 22): Percolation
Lecture 6 (September 27): Percolation
Lecture 7
(September 29 ---
Problem Set 1 due): Percolation
Lecture 8 (October 4): Schramm-Loewner evolution (SLE). See slides by
Tom Alberts and
2006 ICM slides by Oded Schramm and
St. Flour Lecture Notes by Wendelin Werner . See also
Ito's lemma
notes .
Lecture 9 (October 6 -- Project 1 due): See online book on
trees by
Lyons and Peres
Lecture 10 (October 13): SLE
Lecture 11 (October 18): SLE
Lecture 12 (October 20): SLE, see
Schramm's percolation notes
Lecture 13 (October 25): SLE, see Smirnov's ICM slides
Lecture 14 (October 27): SLE
Lecture 15 (November 1): Gaussian free field,
Problem Set 2 due, see
GFF reference
Lecture 16 (November 3): Gaussian free field, Project 2 due
Lecture 17 (November 8): Quantum gravity
Lecture 18 (November 10): Quantum gravity, some slides
Lecture 19 (November 15): Quantum gravity,
Problem Set 3 due. See planar map slides
and Bernardi's slides part 1
and
part 2
.
Lecture 20 (November 17): Quantum gravity
Lecture 21 (November 22): Quantum gravity
Lecture 22 (November 29): Yang-Mills theory. See
Clay problem and
description by Jaffe and Witten . See Wikipedia on Yang Mills and
Lattice
gauge theory and Quantum
chromodynamics and
existence and mass gap problem and Wightman axioms .
Also
Osterwalder-Schrader axioms . Recall definitions of connection and
curvature. See AdS/CFT
note.
Lecture 23 (December 1): Yang-Mills. Consider quantum
harmonic oscillator and Wick rotation and
reflection positivity.
Lecture 24 (December 6): Yang-Mills See construction
of YM with an Infrared cutoff and Balaban I
and
II . Also
Wick's theorem and normal order.
Lecture 25 (December 8): Yang-Mills. Think about SU(n) and
general
compact Lie
algebras and uniform spanning tree.
Lecture 26 (December 13): Yang-Mills. Project 4 due.