Explore the mathematical foundations and universal phenomena in vertex models through this comprehensive workshop featuring leading experts in statistical mechanics, probability theory, and algebraic methods. Delve into the intricate connections between integrable lattice models and their applications in understanding critical phenomena, limit shapes, and convergence behaviors. Examine cutting-edge research on the Ising model, six-vertex models, random cluster models, and stochastic particle systems while discovering how Bethe ansatz, conformal field theory methods, and quantum group techniques contribute to solving complex mathematical problems. Investigate the interplay between algebraic structures such as transfer matrix formalism and diagram algebras with probabilistic approaches including KPZ universality and SLE/CLE theory. Learn about recent developments in dimer models, orthogonal polynomials, arctic curves, and their geometric interpretations through detailed presentations on topics ranging from fermionic Gaussian free fields to shuffle algebras and Macdonald functions. Gain insights into multi-species models, forest fires, sandpile systems, and their connections to broader mathematical frameworks while exploring how these diverse approaches converge to reveal universal mathematical structures across different physical and mathematical contexts.

Syllabus

Hugo Duminil-Copin - Critical phenomena through the lens of the Ising model - Green Family Lecture
Hugo Duminil Copin - Rotational invariance of planar random cluster models... and beyond?
Promit Ghosal - Tail probabilities of the stochastic six vertex model - IPAM at UCLA
Michael Wheeler - A vertex model proof of a correspondence due to Imamura--Mucciconi--Sasamoto
Ivan Corwin - Scaling limit of colored ASEP - IPAM at UCLA
Jeffrey Kuan - Universality of dynamic processes using Drinfel'd twisters - IPAM at UCLA
Alexei Borodinof - Geometry of dimer models - IPAM at UCLA
Harini Desiraju - Elliptic orthogonal polynomials and their integrability - IPAM at UCLA
Jacopo Borga - On the geometry of uniform meandric systems - IPAM at UCLA
Richard Kenyon - On the higher-rank dimer model - IPAM at UCLA
Wioletta Ruszel - Fermionic Gaussian free field and connections to random lattice models
Marianna Russkikh - Perfect t-embedding of uniformly weighted hexagon - IPAM at UCLA
Leonid Petrov - Vertex model integrability for stochastic particle systems - IPAM at UCLA
Vadim Gorin - Six-vertex model in the rare corners regime - IPAM at UCLA
Daniel Remenik - Solving PNG - IPAM at UCLA
Philippe Di Francesco - Arctic curves for vertex models - IPAM at UCLA
Jesper Jacobsen - Exact three- and four-point correlation functions in O(n) and Potts loop models
Tomohiro Sasamoto - Skew RSK dynamics - IPAM at UCLA
Sasha Garbali - Shuffle algebras, lattice paths and Macdonald functions - IPAM at UCLA
David Keating - Stochastic Box-Ball System - IPAM at UCLA
Filippo Colomo - Frozen boundaries and their fluctuations in the square-ice model - IPAM at UCLA
Istvan Prause - Limit shapes of non-intersecting Brownian bridges via harmonic envelope