Positivity for Symmetric Functions and Vertex Models
Explore connections between symmetric function homomorphisms and stochastic six-vertex model positivity, linking to RSK correspondence in algebraic combinatorics.
Perfect t-Embedding of Uniformly Weighted Hexagon
Explore perfect t-embedding of uniformly weighted hexagons in this advanced mathematics lecture, delving into vertex models and their algebraic and probabilistic aspects of universality.
Limit Shapes of Non-Intersecting Brownian Bridges via Harmonic Envelope
Explores limit shapes of non-intersecting Brownian bridges, focusing on macroscopic patterns and connections to random Young tableaux using the tangent plane method and harmonic envelope.
Vertex Model Proof of Imamura-Mucciconi-Sasamoto Correspondence
Explore vertex model proof of q-Whittaker polynomials correspondence, examining lattice path partition functions and their connection to Imamura-Mucciconi-Sasamoto's match between q-Whittaker and periodic Schur measures.
Scaling Limit of Colored Asymmetric Simple Exclusion Process
Explore the scaling limit of colored ASEP using Yang-Baxter equation and Gibbs line ensemble techniques, revealing connections to the KPZ universality class and related probabilistic objects.
Colored Vertex Models, Orthogonal Functions and Probability - Lecture 2
Delve into advanced concepts of colored vertex models, exploring their connections to orthogonal functions and probability theory through expert mathematical analysis and demonstrations.
Shuffle Algebras, Lattice Paths and Macdonald Functions
Explore connections between Macdonald functions, shuffle algebras, and vertex model partition functions in this advanced mathematics lecture on algebraic and probabilistic aspects of universality.
Arctic Curves for Vertex Models
Exploration of arctic curves in 2D integrable lattice models, focusing on 6 Vertex and 20 Vertex models. Discusses phase boundaries, tangent method, and related combinatorial results in tiling problems.
Vertex Model Integrability for Stochastic Particle Systems
Explore integrable stochastic particle systems and their connection to vertex models. Learn about TASEP, Yang-Baxter equations, and applications in mathematics and biology.
Six-Vertex Model in the Rare Corners Regime
Explore limit shapes in six-vertex models, focusing on low-density corner scenarios. Discover new features, hyperbolic PDEs, density discontinuities, and connections to random permutations.
On the Higher-Rank Dimer Model
Richard Kenyon explores the higher-rank dimer model, discussing GL(n) local systems, Kasteleyn operators, and n-multiwebs. He presents scaling limit results for SL(3) and their conformal invariance in this advanced mathematics talk.
Conformal Field Theory Approach to Quantum Loop Models
Explore conformal field theory's application to quantum loop models, uncovering connections between statistical mechanics and quantum field theory.
An Ising-Type Formulation of the Six-Vertex Model
Explore integrability in condensed matter physics and quantum field theory through an Ising-type formulation of the six-vertex model.
Vertex Model for Tissue Mechanics - Part I
Explore vertex models for tissue mechanics, focusing on fundamental concepts and applications in biological systems.
Growth and Mechanics of Tissues - SPL Rothschild Lecture
Explorez les propriétés mécaniques des tissus et leur rôle dans la croissance et l'expression génétique, en mettant l'accent sur les tissus cancéreux et le développement précoce.
Colored Vertex Models, Orthogonal Functions and Probability - Lecture 1
Explore the intersection of colored vertex models, orthogonal functions, and probability theory through advanced mathematical concepts in discrete integrable systems and statistical physics.
Lower Tail Large Deviations for the Stochastic Six Vertex Model
Explore advanced mathematical concepts in discrete integrable systems, focusing on stochastic six vertex models and their large deviation principles through theoretical physics and probability theory.