This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include:
Yang-Baxter equation The restricted Siegel disc and restricted Grassmannian Geometric and deformation quantization Degenerate integrability Lie algebroids and groupoids Skew braces
Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
Preface.- 40 years of the Workshop with Anatol Odzijewicz.- Wigner Medal 2023.- Part I. Session in memory of Anatol Odzijewicz.- On the geometry of coherent state maps.- Groupoid techniques in operator theory.- Integrable system on partial isometries: a finite dimensional picture.- The restricted Siegel disc as coadjoint orbit.- Geometric quantization (55 years later).- Deformation of Functions by Star Product.- Part II. Session: Facets of the Yang-Baxter Equation.- Special normalised affine matrices. An example of a Lie affgebra.- Twisted Araki–Woods Algebras, the Yang–Baxter Equation, and quantum field theory.- Skew braces and the braid equation on sets.- Skew braces: a brief survey.- Part III. General contributions on geometric methods in physics.- How birefringence arises from nonlinear electrodynamics.- Lp-Cuntz algebras and spectrum of weighted composition operators.- On Automorphisms of Complex bk-Manifolds.- Spherical pedal coordinates and calculus of variations.- Higher order curvature corrections in the Raychaudhuri equation.- Yangians as pre-Lie and tridendriform algebras.- Hermite–Padé approximation, multiple orthogonal polynomials, and multidimensional Toda equations.- “The six blind men and the elephant”: An interdisciplinary selection of measurement features.- Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of compact Lie groups.- A quadric of kinetic energy in the role of phase diagrams – application to the Belinski-Khalatnikov-Lifshitz scenario.- Hamiltonian structure of isomonodromic deformation dynamics in linear systems of PDE’s.- Discrete mechanics in non-uniform time α-lattices.- Quantum Derivation and Mishchenko-Fomenko Construction.- The Milgromian acceleration of MOND and the cosmological constant from precanonical quantum gravity.- A note on three collinear point charges.- Conceptual Problems in Quantum Squeezing.- Lie Symmetry Analysis of the Charney- Hasegawa-Mima equation.- Stability Theorem for Zn2-Lie supergroups.- The Courant type algebroids, the coadjoint orbits and related integrable flows.- Part IV. Abstract of a Lecture at “XII School on Geometry and Physics”.- Kronecker webs and nonlinear PDEs.- Index.
