Random Tilings Workshop: February 18 – 22, 2013

 

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 Poster

Random Tilings Workshop Schedule

Time Title Presenters  Video
10:15am A third-order phase transition in random tilings Fillipo Colomo video
slides 
11:30am Solvable incommensurable random tilings Bernard Nienhuis video
slides
12:30pm Lunch
 2:30pm Asymptotics of symmetric functions with applications in statistical mechanics Greta Panova video
slides 
 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
slides
11:30am Two boundary refinement of the Razumov-Stroganov correspondence Luigi Cantini video
slides
12:30pm Lunch
 3:00pm The 2-boundary Brauer mode Anita Ponsaing video
slides
 3:30pm Tea Time
 4:00pm TBA Paul Zinn-Justin video
slides 
 5:30pm Complimentary to participants Wine and Cheese Reception  
 6:00pm  For more info: http://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
slides
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
slides 
 12:30  Lunch
 2:00pm Critical Temperature of Periodic Ising Models Zhongyang Li video
slides 
 2:30pm Skew plane partitions with non-homogeneous weights Sevak Mkrtchyan video
slides 
 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
slides 
11:30am Tilings, Point sets, and Dynamical Systems Christoph Richard video
slides 
12:30pm Lunch
 2:00pm Bethe vectors and solutions to the reflections q-KZ equation Nicolai Reshetikhin video
slides 
 3:00pm Six vertex model: A counterexample in statistical mechanics Vladimir Korepin video
slides 
 3:30pm Tea Time
 4:00pm Special polynomials related to elliptic lattice models and Painlevé VI Hjalmar Rosengren video
slides 
 5:30pm Complimentary to participants Wine and Cheese Reception
 6:00pm  For more info: http://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
slides
10:15am From tilings to general-beta matrix ensembles: appearance of the Gaussian Free Field Vadim Gorin video
slides
11:30am Random tilings of polygons by rhombi, and their Gaussian Free Field fluctuations Leonid Petrov video
slides
12:00pm The Virasoro algebra and discrete Gaussian free field Fredrik Viklund video
slides
12:30pm Lunch
 3:30pm Tea Time