Gaussian free field in random tilings
The fluctuations of the height function of random lozenge and domino tilings of polygonal domains are believed to be governed by the 2d Gaussian Free Field in an appropriate complex structure. This was conjectured by Kenyon and Okounkov and they also suggested a neat geometric procedure for defining the corresponding complex structure.
I will present a new approach to this conjecture for a class of domains through gluings of Gelfand-Tsetlin patterns. It combines discrete Dyson-Schwinger equations with the method of Schur generating functions to yield the result.
Professor Vadim Gorin, MIT