This book contains the proceedings of two international conferences: a satellite meeting of the IUPAP Statphys-19 Conference and the Seventh Nankai Workshop, held in Tianjin, China in August 1995. The central theme of the two conferences, which drew participants from 18 countries, was the Yang–Baxter equation and its development and applications. With topics ranging from quantum groups, vertex and spin models, to applications in condensed matter physics, this book reflects the current research interest of integrable systems in statistical mechanics. Contents:Satellite Meeting of Statphys-19:Boundary Yang–Baxter in the RSOS/SOS Representation (C Ahn & W M Koo)Quantum Domains in Ferromagnetic Anisotropic Heisenberg Chains (F C Alcaraz et al.)The Generalized Chiral Clock Model and Its Phase Diagram (H Au-Yang & J H H Perk)Algebraic Solution of the Coincidence Problem for Crystals and Quasicrystals (M Baake)Reflection Equations and Surface Critical Phenomena (M T Batchelor)Quantum Field Theories in Terms of Group-Valued Local Fields: An Overview (L-L Chau)U(1)-Invariant Local and Integrable Lattice Formulation of the Massive Thirring Model (C Destri)Dilute Algebras and Solvable Lattice Models (U Grimm)Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition (Y Hatsugai et al.) Quantum Group and the Hofstadter Problem (Y Hatsugai et al.)Domain Walls in the Spin-S Quantum Ising Chain (M Henkel)Probability of Phase Separation and Two Point Temperature Correlation Functions for the Bose Gas with Delta Interaction (A R Its & V E Korepin)Stochastic Reaction-Diffusion Processes, Operator Algebras and Integrable Quantum Spin Chains (G M Schütz)Vertex-Face Correspondence in Elliptic Solutions of the Yang–Baxter Equation (Y Shibukawa)Logarithmic Anomalies of Susceptibility for Solvable Models (M Takahashi)On Chiral Hubbard Model at Strong Interaction (D F Wang)Soluble Free-Fermion Models in d Dimensions (F Y Wu)Bosonization Based on Bethe Ansatz Equations and Proof of the Conformal Conjecture (Y-S Wu & Y Yu)and other papersThe Seventh Nankai Workshop:Corner Transfer Matrix of Asymmetric Vertex Models (H-P Eckle)Scaling Properties of the Ising Model in a Field (U Grimm & B Nienhuis)One Dimensional Lattice Models of Electrons with r–2 Hopping and Exchange (Ch Gruber & D F Wang)Symmetry Group Invariants for Spontaneous Magnetization (J-M Maillard)Experimental Realizations of Integrable Reaction-Diffusion Processes in Biological and Chemical Systems (G M Schütz)Zamolodchikov–Faddeev Algebra in 2-Component Anyons (Y-L Shen & M-L Ge)and other papers Readership: Theoretical physicists and mathematicians. keywords:

This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

This volume contains the proceedings of the conference on Formal and Analytic Solutions of Diff. Equations, held from June 28–July 2, 2021, and hosted by University of Alcalá, Alcalá de Henares, Spain. The manuscripts cover recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, moment differential equations, etc. Also discussed are related topics such as summability of formal solutions and the asymptotic study of their solutions. The volume is intended not only for researchers in this field of knowledge but also for students who aim to acquire new techniques and learn recent results.