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.