Organized by Rick Kenyon, Jan de Gier, and Bernard Nienhuis
Random tilings in two dimensions provide an interesting class of discrete geometric models that exhibit critical behavior and hence are expected to be described by conformal eld theories and SLEs. The random tiling of lozenges, being free fermionic and describable in terms of nonintersecting lattice paths, can be analyzed in great detail using techniques of solvable lattice models, combinatorics and random matrix theory. This workshop intends to study more complex random tiling models that go beyond the class of free fermion models. Such tilings can still be Bethe Ansatz integrable, such as a class of rectangle triangle tiling models discovered in the late nineties. More recently these tilings have gained renewed interest due to the connection of the square triangle tiling with Littlewood Richardson coefficient from representation theory, as discovered by Knutson and Tao. Interested participants include Andrei Okounkov, Paul Zinn-Justin and others.
This workshop is a part of the Spring 2013 program Conformal Geometry, Organized by Ilia Binder, John Cardy, Andrei Okounkov, and Paul Wiegmann
Attendee List Schedule PDF Download PosterView Videos
Random Tilings Workshop Schedule
Time | Title | Presenters | Video |
10:15am | A third-order phase transition in random tilings | Fillipo Colomo | video |
11:30am | Solvable incommensurable random tilings | Bernard Nienhuis | video |
12:30pm | Lunch | ||
2:30pm | Asymptotics of symmetric functions with applications in statistical mechanics | Greta Panova | video |
3:30pm | Tea Time | ||
4:00pm | Boxed plane partitions and Aztec diamond via Schur and Macdonald processes | Dan Betea | video |
Time | Title | Presenters | Video |
10:15am | Connectivity patterns in loop percolation and constant term identities | Dan Romik | video |
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12:30pm | Lunch | ||
3:00pm | The 2-boundary Brauer mode | Anita Ponsaing | video |
3:30pm | Tea Time | ||
4:00pm | TBA | Paul Zinn-Justin | video |
5:30pm | Complimentary to participants | Wine and Cheese Reception | |
6:00pm | For more info: https://scgp.stonybrook.edu/archives/6359 | Materializing Information Gallery Closing |
Time | Title | Presenters | Video |
9:15am | Local statistics of the abelian sandpile model | David Wilson | video |
10:15am | Discrete Orthogonal Polynomial Ensembles arising in Random Tiling Problems and the discrete Painleve equations | Nicholas Witte | video |
11:30pm | Quantum Painleve Cubics | Marta Mazzocco | video |
12:30 | Lunch | ||
2:00pm | Critical Temperature of Periodic Ising Models | Zhongyang Li | video |
2:30pm | Skew plane partitions with non-homogeneous weights | Sevak Mkrtchyan | video |
3:30pm | Tea Time | ||
5:30pm | Complimentary to participants | Wine and Cheese Reception | |
6:30pm | Banquet Dinner for Workshop Participants |
Time | Title | Presenters | Video |
10:15am | Classification of patterns in the deterministic Abelian Sandpile Model | Andrea Sportiello | video |
11:30am | Tilings, Point sets, and Dynamical Systems | Christoph Richard | video |
12:30pm | Lunch | ||
2:00pm | Bethe vectors and solutions to the reflections q-KZ equation | Nicolai Reshetikhin | video |
3:00pm | Six vertex model: A counterexample in statistical mechanics | Vladimir Korepin | video |
3:30pm | Tea Time | ||
4:00pm | Special polynomials related to elliptic lattice models and Painlevé VI | Hjalmar Rosengren | video |
5:30pm | Complimentary to participants | Wine and Cheese Reception | |
6:00pm | For more info: https://scgp.stonybrook.edu/archives/6042 | Nowhere Differentiable Gallery Closing Reception |
Time | Title | Presenters | Video |
9:30am | Connective constant for a weighted self-avoiding walk on a rhombi tiling | Alexander Glazman | video |
10:15am | From tilings to general-beta matrix ensembles: appearance of the Gaussian Free Field | Vadim Gorin | video |
11:30am | Random tilings of polygons by rhombi, and their Gaussian Free Field fluctuations | Leonid Petrov | video |
12:00pm | The Virasoro algebra and discrete Gaussian free field | Fredrik Viklund | video |
12:30pm | Lunch | ||
3:30pm | Tea Time | ||