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Six-vertex model, dimers, shapes, and all that: March 14 – 18, 2016

Organized by: Pavel Bleher, Vladimir Korepin and Bernard Nienhuis

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Dates: March 14-18, 2016

The workshop will be devoted to recent results on the six-vertex and related models. The bulk free energy in the six-vertex model was explicitly calculated for periodic boundary conditions by Lieb. Then other boundary conditions were studied. A very interesting case is the domain wall boundary conditions (DWBC). The six-vertex model provides an important ‘counterexample’ in statistical mechanics: the bulk free energy in the thermodynamic limit depends on boundary conditions. In particular, it is different for periodic and domain wall boundary conditions. The dimer model on the Aztec diamond is a special case of the six-vertex model, as well as the square ice model, ferroelectric and antiferroelectric models, ensembles of alternating sign matrices, and others.

The partition function of the six-vertex model with DWBC in a finite box has been expressed, via the Yang-”Baxter equations, in terms of a Hankel determinant. It can be furthermore expressed as a partition function of an ensemble of random matrices with a non-polynomial interaction. This expression was used, via the powerful Riemann-Hilbert approach, to obtain the asymptotic behavior of the partition function of the six-vertex model with DWBC in different phase regions.

The remarkable observation by Razumov and Stroganov which links some observables on the square grid to those on the half-infinite cylinder is a subject of active research. It appears to admit generalizations to other geometries and other models


Talk Schedule

Time Title Speaker Location
 9:00 am Welcome Address Pavel Bleher SCGP 102
 9:10 am Edge-tacnode phenomena in random tilings  Pierre Van Moerbeke SCGP 102
 10:00 am Coffee Break N/A SCGP Lobby
 10:30 am A one-point function in 4D N=4 supersymmetric Yang-Mills using six-vertex model methods Omar Foda SCGP 102
 11:20 am Asymmetric simple exclusion process with open boundaries and Koornwinder polynomials Luigi Cantini SCGP 102
 12:10 pm Lunch N/A SCGP Café
 2:00 pm Classification of quantum groups of Kulish-Reshetikhin type Alexander Stolin SCGP 102
 2:50 pm Influence of boundary conditions on bulk properties of six-vertex model Giuliano Ribeiro SCGP 102
 3:40 pm Coffee Break N/A SCGP Lobby
 4:10 pm Prefundamental representations and Q-operators Carlo Meneghelli SCGP 102

Time Title Speaker Location
 9:00 am Stochastic higher-spin vertex models and their self-duality. Ivan Corwin SCGP 102
 9:50 am Coffee Break N/A SCGP Lobby
 10:20 am Elliptic pfaffians and solvable lattice models  Hjalmar Rosengren SCGP 102
 11:10 am Equilibrium measures and limit shapes revisited. Jonathan Novak SCGP 102
 12:00 pm Lunch  N/A SCGP Café
1:00 pm SCGP Weekly Talk: “The six vertex model and randomly growing interfaces in (1+1) dimensions” Alexei Borodin  SCGP 102
 2:10 pm Arctic curve of the six-vertex model in an L-shaped domain Filippo Colomo SCGP 102
 3:00 pm The mother body phase transition in the normal matrix model Guilherme Silva SCGP 102
 3:40 pm Coffee Break N/A SCGP Lobby
 4:10 pm Large-degree asymptotics of rational Painleve functions Robert Buckingham SCGP 102

Time Title Speaker Location
 9:00 am Conserved currents and discrete holomorphicity in vertex and face models  Robert Weston SCGP 102
 9:50 am  Coffee Break  N/A SCGP Lobby
 1020 am  Paul Zinn-Justin SCGP 102
 11:10 am Rigorous analysis of the 6-vertex model  Tony Dorlas SCGP 102
 12:00 pm  Lunch  N/A SCGP Café
 2:00 pm How to invert the Kasteleyn matrix of the 2-periodic Aztec diamond  Benjamin Young SCGP 102
 2:50 pm At the `liquid-gas’ boundary of the two-periodic Aztec diamond  Sunil Chhita SCGP 102
 3:40 pm  Coffee Break  N/A SCGP Lobby
 4:10 pm Smallest singular value distribution and large gap asymptotics for products of random matrices  Manuela Girotti SCGP 102


Time Title Speaker Location
 9:00 am Dimers and Geometry Richard Kenyon SCGP 102
 9:50 am  Coffee Break  N/A SCGP Lobby
 10:20 am The six-vertex model on a hexagon  Ivan Kostov SCGP 102
 11:10 am Lozenge tilings with symmetries  Greta Panova SCGP 102
 12:00 pm  Lunch  N/A SCGP Café
 2:00 pm Exponential jump model in continuous inhomogeneous medium  Leonid Petrov SCGP 102
2:50 pm Lozenge tilings: universal bulk limits, global fluctuations and all that  Vadim Gorin SCGP 102
 3:40 pm  Coffee Break  N/A SCGP Lobby
4:10 pm The spin-one XXZ chain and symmetry classes of alternating sign matrices Christian Hagendorf SCGP 102

Time Title Speaker Location
 9:00 am Loop models and skein theory  Jasper Stokman SCGP 102
 9:50 am  Coffee Break  N/A SCGP Lobby
 10:20 am Higher rank generalisations of the six vertex model and Macdonald-Koornwinder polynomials Michael Wheeler SCGP 102
 11:10 am  Karl Liechty SCGP 102
 12:00 pm  Lunch  N/A SCGP Café
 2:00 pm Deformations of the Tracy-Widom distribution and transition asymptotics for Painleve II  Thomas Bothner SCGP 102
 2:50 pm Dimer Models and Block Toeplitz Determinants Estelle Basor SCGP 102
 3:40 pm  Coffee Break  N/A SCGP Lobby


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