Symmetric Functions: Foundations and Applications in Combinatorics - Part 1
Explore symmetric functions in algebraic combinatorics, representation theory, and statistical mechanics. Learn formulas, combinatorial models, and key properties with applications and open problems.
Dimer Models and Random Tilings - Part 1
Explore dimer models and random tilings with Cédric Boutillier. Learn about Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for studying perfect matchings on lattices.
Perfect t-embeddings of Uniform Aztec Diamond Graphs
Explores t-embeddings of uniform Aztec diamond graphs, providing new formulas and asymptotic analysis to prove convergence of dimer model height fluctuations to a Gaussian Free Field.
Dimer Models and Random Tilings - Part 2
Explore dimer models, perfect matchings, and tilings with advanced mathematical tools. Delve into Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for large-scale limits.
Symmetric Functions: Formulas, Combinatorial Models, and Applications - Part 2
Explore advanced concepts in symmetric functions, their applications in combinatorics and representation theory, and their role in statistical mechanics as partition functions.
On Variants of Specht Polynomials and Random Geometry
Explore connections between Specht polynomials, conformal field theory, and random geometry. Discover algebraic structures in statistical mechanics models and their geometric interpretations.
Dimers and M-curves: Limit Shapes from Riemann Surfaces
Explore dimer models, M-curves, and limit shapes through algebraic geometry, integrating Riemann surfaces and Schottky uniformization. Gain insights into statistical mechanics and discrete geometry.
Spectrum of Sparse Inhomogeneous Random Graphs
Explore the spectrum of sparse inhomogeneous random graphs, examining structural properties and applications in network science, probability theory, and statistical physics.
Well Posedness for Hamilton-Jacobi Equations for Linearly Controlled Gradient Flows
Explore well-posedness of Hamilton-Jacobi equations for linearly controlled gradient flows, examining mathematical foundations and applications in optimization and control theory.
Incidences and Dimers in Projective Geometry - Statistical Mechanics and Discrete Geometry
Explore the connection between linear incidence theorems in projective geometry and bipartite graphs on surfaces, incorporating dimer model dynamics to derive dynamic linear incidence theorems.
Using Topology - Fundamental Forces and Nonequilibrium Potentials by Massimiliano Esposito
Explore fundamental forces and nonequilibrium potentials in topology, uncovering insights into energy flows, constraints, and limits in cellular processes and bioenergetics.
Random Matrix Statistics in the Uniform Spanning Tree
Explore random matrix statistics in uniform spanning trees, focusing on branch behavior, scaling limits, and connections to Dyson Brownian motion and Loewner evolution.
Superport Networks: Generalizing Kirchhoff's Matrix-Tree Theorem
Exploration of multiport networks, generalizing Kirchhoff's theorem with novel mathematical approaches. Insights into electrical engineering applications and superport network theory.
Geometric Objects Associated to Planar Bipartite Graphs
Explore topological and geometric data associated with planar bipartite graphs, including knots, cluster varieties, and critical varieties, and their interconnections.
Planar Site Percolation via Tree Embeddings
Explore planar site percolation and tree embeddings in infinite graphs. Discover novel proofs for Bernoulli percolation and confirm a 1996 conjecture by Benjamini and Schramm.
Scaling Exponents in Stationary Random Graphs
Explore scaling exponents in stationary random graphs, examining relationships between fractal dimension, walk dimension, resistance, spectral dimension, and extremal growth in statistical physics.
Branching Random Walks on Zd for d ≥ 4 - Excess Folding and Branching Capacity
Explore estimates for excess folding in Branching Random Walks and the role of branching capacity in higher dimensions, presented by Amine Asselah at IPAM's Statistical Mechanics Workshop.
Sharp Threshold for Rigidity of Random Graphs
Explore the evolution of random graphs and discover key moments when they become rigid and globally rigid, with implications for vertex embedding and distance preservation.
Cutoff for Biased Transpositions in Card Shuffling
Explore card shuffling algorithms and mixing times with biased transpositions, extending Diaconis and Shahshahani's work on random transpositions in deck shuffling.
Minkowski Content of the Scaling Limit of 3D Loop-Erased Random Walk
Explores Minkowski content of 3D loop-erased random walk's scaling limit, focusing on discrete space analysis, one-point function estimates, and ball-hitting probabilities in Z^3.
Random Aggregation on the Complex Plane and the Hastings-Levitov Models
Explore random aggregation on complex planes through ALE models, including Hastings-Levitov models. Discover scaling limits, fluctuations, and connections to fundamental discrete models in statistical mechanics.