Setting the scene: Introduction to domino tiling and the dimer model, height function, and Gaussian free fields. Stated (and clarified) Kenyon's theorems on conformal invariance of height variation, and the convergence of height variation to GFF.

2/10

Conformal invariance of domino tiling, Part II

Joe Chen

Changed:

< <

Covered Kasteleyn matrix, coupling function, convergence of the coupling function to $F_0, F_1$, which transform analytically under conformal maps.

> >

Covered Kasteleyn matrix, coupling function (a Cauchy kernel), convergence of the coupling function to $F_0, F_1$, which transform analytically under conformal maps.

2/17

Dominos and the Gaussian Free Field

Joe Chen

Changed:

< <

Will finish showing how $F_0, F_1$ enter into the moment formula of the height function. Then convergence to GFF

> >

Will clarify the connection between the coupling function and the Green's function. The rest is to show how $F_0, F_1$ enter into the moment formula of the height function, from which convergence to GFF is proved.

2/24

Discrete complex analysis

Baris Ugurcan

Further topics TBD: A session devoted to potential theory & harmonic measures may be in the offing.