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10:00
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16:00
›9:30 (45min)
Vadim Gorin - Boundary limits for the six-vertex model
Take a random configuration of (a,b,c)-weighted six-vertex model in a very large planar domain. What does it look like near a straight segment of the boundary? We investigate this question on the example of the model in N*N square with Domain Wall Boundary Conditions and find that the answer depends on the value of \Delta=(a^2+b^2-c^2)/(2ab): there is a single universal limiting object for all \Delta<1 and a richer class of limits at \Delta>1.
Take a random configuration of (a,b,c)-weighted six-vertex model in a very large planar domain. What does it look like near a straight segment of the boundary? We investigate this question on the example of the model in N*N square with Domain Wall Boundary Conditions and find that the answer depends on the value of \Delta=(a^2+b^2-c^2)/(2ab): there is a single universal limiting object for all \Delta<1 and a richer class of limits at \Delta>1.
› Amphi 15
9:30 - 10:15 (45min)
Vadim Gorin - Boundary limits for the six-vertex model
Amphi 15
Take a random configuration of (a,b,c)-weighted six-vertex model in a very large planar domain. What does it look like near a straight segment of the boundary? We investigate this question on the example of the model in N*N square with Domain Wall Boundary Conditions and find that the answer depends on the value of \Delta=(a^2+b^2-c^2)/(2ab): there is a single universal limiting object for all \Delta<1 and a richer class of limits at \Delta>1.
›10:15 (45min)
Terrence George - Move-reduced graphs on a torus
We determine which bipartite graphs embedded in a torus are move-reduced. In addition,we classify equivalence classes of such move-reduced graphs under square/spider moves.This extends the class of minimal graphs on a torus studied by Goncharov–Kenyon, and gives a toric analog of Postnikov’s results on a disk. Joint work with Pavel Galashin
We determine which bipartite graphs embedded in a torus are move-reduced. In addition,we classify equivalence classes of such move-reduced graphs under square/spider moves.This extends the class of minimal graphs on a torus studied by Goncharov–Kenyon, and gives a toric analog of Postnikov’s results on a disk. Joint work with Pavel Galashin
› Amphi 15
10:15 - 11:00 (45min)
Terrence George - Move-reduced graphs on a torus
Amphi 15
We determine which bipartite graphs embedded in a torus are move-reduced. In addition,we classify equivalence classes of such move-reduced graphs under square/spider moves.This extends the class of minimal graphs on a torus studied by Goncharov–Kenyon, and gives a toric analog of Postnikov’s results on a disk. Joint work with Pavel Galashin
›11:00 (30min)
11:00 - 11:30 (30min)
Coffee break
›11:30 (45min)
Catherine Wolfram - Large deviations for the 3D dimer model
A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. I will explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments. Time permitting, I will also explain some stories that illustrate qualitative differences between two and three dimensions.
A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. I will explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments. Time permitting, I will also explain some stories that illustrate qualitative differences between two and three dimensions.
› Amphi 15
11:30 - 12:15 (45min)
Catherine Wolfram - Large deviations for the 3D dimer model
Amphi 15
A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. I will explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments. Time permitting, I will also explain some stories that illustrate qualitative differences between two and three dimensions.
›12:15 (45min)
Marcin Lis - Conformal invariance of critical double random currents
The double random current (DRC) model is a natural percolation model whose geometric properties are intimately related to spin correlations of the Ising model. In two dimensions, it moreover carries an integer valued height function on the graph, called the nesting field. We study the critical DRC model on bounded domains of the square lattice. We fully describe the joint scaling limit of the (primal and dual) DRC clusters and the nesting field as the lattice mesh size vanishes. We prove that the nesting field becomes the Dirichlet Gaussian free field (GFF) in this limit, and that the outer boundaries of the DRC clusters with free boundary conditions are the conformal loop ensemble with $\kappa =4$ (CLE4) coupled to that GFF. Moreover, we also show that the inner boundaries of the DRC clusters form a two-valued local set with values $\mp 2\lambda,(2 \sqrt 2 \mp 2)\lambda$ for the field restricted to a CLE4 loop with boundary value $\pm 2\lambda$. Our proof is a combination of
The double random current (DRC) model is a natural percolation model whose geometric properties are intimately related to spin correlations of the Ising model. In two dimensions, it moreover carries an integer valued height function on the graph, called the nesting field. We study the critical DRC model on bounded domains of the square lattice. We fully describe the joint scaling limit of the (primal and dual) DRC clusters and the nesting field as the lattice mesh size vanishes. We prove that the nesting field becomes the Dirichlet Gaussian free field (GFF) in this limit, and that the outer boundaries of the DRC clusters with free boundary conditions are the conformal loop ensemble with $\kappa =4$ (CLE4) coupled to that GFF. Moreover, we also show that the inner boundaries of the DRC clusters form a two-valued local set with values $\mp 2\lambda,(2 \sqrt 2 \mp 2)\lambda$ for the field restricted to a CLE4 loop with boundary value $\pm 2\lambda$. Our proof is a combination of
› Amphi 15
12:15 - 13:00 (45min)
Marcin Lis - Conformal invariance of critical double random currents
Amphi 15
The double random current (DRC) model is a natural percolation model whose geometric properties are intimately related to spin correlations of the Ising model. In two dimensions, it moreover carries an integer valued height function on the graph, called the nesting field. We study the critical DRC model on bounded domains of the square lattice. We fully describe the joint scaling limit of the (primal and dual) DRC clusters and the nesting field as the lattice mesh size vanishes. We prove that the nesting field becomes the Dirichlet Gaussian free field (GFF) in this limit, and that the outer boundaries of the DRC clusters with free boundary conditions are the conformal loop ensemble with $\kappa =4$ (CLE4) coupled to that GFF. Moreover, we also show that the inner boundaries of the DRC clusters form a two-valued local set with values $\mp 2\lambda,(2 \sqrt 2 \mp 2)\lambda$ for the field restricted to a CLE4 loop with boundary value $\pm 2\lambda$. Our proof is a combination of
›13:00 (1h30)
13:00 - 14:30 (1h30)
Lunch
›14:30 (45min)
Sunil Chhita - The Two-Periodic Aztec diamond
Domino tilings of the two-periodic Aztec diamond exhibit interesting statistical mechanical behaviors – a limit shape emerges separating three macroscopic interfaces, known as frozen, rough and smooth that depend on the local statistics. We survey some of the main results on this model, as well as recent progress on understanding the rough-smooth boundary. This is based on joint work with Duncan Dauvergne and Thomas Finn.
Domino tilings of the two-periodic Aztec diamond exhibit interesting statistical mechanical behaviors – a limit shape emerges separating three macroscopic interfaces, known as frozen, rough and smooth that depend on the local statistics. We survey some of the main results on this model, as well as recent progress on understanding the rough-smooth boundary. This is based on joint work with Duncan Dauvergne and Thomas Finn.
14:30 - 15:15 (45min)
Sunil Chhita - The Two-Periodic Aztec diamond
Domino tilings of the two-periodic Aztec diamond exhibit interesting statistical mechanical behaviors – a limit shape emerges separating three macroscopic interfaces, known as frozen, rough and smooth that depend on the local statistics. We survey some of the main results on this model, as well as recent progress on understanding the rough-smooth boundary. This is based on joint work with Duncan Dauvergne and Thomas Finn.
›15:15 (45min)
Nathanaël Berestycki - Near-critical dimers and massive SLE
A programme initiated by Makarov and Smirnov is to describe near-critical scaling limits of planar statistical mechanics models in terms of massive SLE and/or Gaussian free field. We consider here the dimer model on the square or hexagonal lattice with doubly periodic weights, which is known to have non Gaussian limits in the whole plane. In joint work with Levi Haunschmid (TU Vienna) we obtain the following results: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov; (b) we show that the convergence of the height function in arbitrary bounded domains subject to Temperleyan boundary conditions, and that the scaling limit is universal; and (c) we prove conformal covariance of the scaling limit. Our techniques rely on Temperley's bijection and the
A programme initiated by Makarov and Smirnov is to describe near-critical scaling limits of planar statistical mechanics models in terms of massive SLE and/or Gaussian free field. We consider here the dimer model on the square or hexagonal lattice with doubly periodic weights, which is known to have non Gaussian limits in the whole plane. In joint work with Levi Haunschmid (TU Vienna) we obtain the following results: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov; (b) we show that the convergence of the height function in arbitrary bounded domains subject to Temperleyan boundary conditions, and that the scaling limit is universal; and (c) we prove conformal covariance of the scaling limit. Our techniques rely on Temperley's bijection and the
› Amphi 15
15:15 - 16:00 (45min)
Nathanaël Berestycki - Near-critical dimers and massive SLE
Amphi 15
A programme initiated by Makarov and Smirnov is to describe near-critical scaling limits of planar statistical mechanics models in terms of massive SLE and/or Gaussian free field. We consider here the dimer model on the square or hexagonal lattice with doubly periodic weights, which is known to have non Gaussian limits in the whole plane. In joint work with Levi Haunschmid (TU Vienna) we obtain the following results: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov; (b) we show that the convergence of the height function in arbitrary bounded domains subject to Temperleyan boundary conditions, and that the scaling limit is universal; and (c) we prove conformal covariance of the scaling limit. Our techniques rely on Temperley's bijection and the
