Schedule: We meet on Fridays from 10:30am (sharp!) until 12, in 1011 Evans.

• Friday, 3 February. Introduction to the Gaussian Free Field. (Gabor Pete)
  See Scott Sheffield's GFF for mathematicians -- with additional fun information supplied by Gabor.
• Friday, 10 February. Introduction to the Gaussian Free Field, continued (Gabor Pete)
  
• Friday, 17 February. Local Statistics of Lattice Dimers. (Manjunath Krishnapur)
  We'll learn how to compute enough about dimer configurations to start on the Conformal Invariance of Domino Tiling.
• Friday, 24 February. Conformal invariance of domino tiling, and convergence to the Gaussian free field. (Asaf Nachmias)
  See Conformal Invariance of Domino Tiling and Dominos and the GFF, by Rick Kenyon.
• Friday, 3 March. (Peter Ralph) Conformal invariance of domino tiling, and convergence to the Gaussian free field, continued.
  The role of boundary conditions and connections to SLE(8), with pictures.
• Friday, 10 March. (Peter Ralph) Conformal invariance of domino tiling, and convergence to the Gaussian free field, continued.
  Discrete analytic functions, various Green's functions, the moment formula, and the GFF.
• Friday, 17 March. Spanning Trees and Domino Tilings. (Nathan Levy)
  Some material from Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances by R. Burton and R. Pemantle.
• Friday, 24 March. (Gabor Pete and Peter Ralph) Domino tilings, and random curves.
  The final remarks connecting the height function to the Gaussian Free Field, and a proof that the contours given by two overlapping independent domino tilings (conjectured to converge to SLE(4)) are a.s. all finite.
• Friday, 31 March. Spring Break.
• Friday, 7 April. (Manjunath Krishnapur) the Brownian loop soup.
  See the Brownian loop soup by G. Lawler and W. Werner.
• Friday, 14 April. (Aubrey Clayton) Self-avoiding loops.
  See The conformally invariant measure on self-avoiding loops by W. Werner.
• Friday, 21 April. No meeting, because of the Bloomington meetings.
  
• Friday, 28 April. (Dapeng Zhan) Quasi-SLE and lattice models in multiply-connected domains.
  The defintion of some natural analogues of the friendly family of SLEs (2,4,6, and 8) in multiply connected domains. See the slides on Dapeng's home page, and be prepared to ask for more detail in your favorite topics.
• Friday, 5 May 1-2:30pm. (Dapeng Zhan) Continued from last week.
  
• Friday, 12 May. (Gabor Pete) Level curves in the GFF and SLE.
  Outline of the relationship between level curves in the Gaussian free field (and how to make sense of this) and SLE. Based on a series of talks given by Scott Sheffield describing upcoming work. Email the organizers for more background if desired.

Here is the schedule, with links to papers, from last semester.

Related courses:

• Conformally Invariant Critical Systems of Statistical Physics and SLEs, by Fraydoun Rezakhanlou, TTh 12:30-2.
• Topics in Statistical Mechanics, Combinatorics, and Representation Theory, by Nicolai Reshetikhin. syllabus, MWF 12-1.

Related papers:

• GFF for mathematicians by Scott Sheffield

• The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice by P. Kastelen.
• Local statistics of lattice dimers by Rick Kenyon
• Conformal invariance of domino tiling by Rick Kenyon
• Dominos and the GFF by Rick Kenyon
• Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances by R. Burton and R. Pemantle.

• Random Surfaces: Large Deviations Principles and Gradient Gibbs Measure Classifications by Scott Scheffield.
• Dimers and amoebae by Richard Kenyon, Andrei Okounkov, Scott Sheffield.

• Basic properties of discrete analytic functions by R.J. Duffin.
• Discrete Analytic Functions: a survey by Laszlo Lovasz
• The asymptotic determinant of the discrete Laplacian by Rick Kenyon.
• The Laplacian and Dirac operators on critical planar graphs by Rick Kenyon.

• The conformally invariant measure on self-avoiding loops. by Wendelin Werner.
• Some recent aspects of random conformally invariant systems by Wendelin Werner.

• A list of papers from the course on domino tilings taught by Marek Biskup at UCLA.
• The Scaling Limit Geometry of Near-Critical 2D Percolation. by F. Camia, L. R. G. Fontes, C. M. Newman.
• Entropic repulsion for the lattice free field: The two dimensional case by E. Bolthausen, J.D. Deuschel, G. Giacomin.
• Critical behavior of the massless free field at the depinning transition. Erwin Bolthausen, Yvan Velenik.
• Dapeng Zhan's home page, with links to some papers about SLE on Riemann surfaces.