Full Description
This volume collects papers based on lectures given at the XLI Workshop on Geometric Methods in Physics, held in Białystok, Poland in July 2024 as well as extended abstracts of minicourses presented during the XIII School on Geometry and Physics. These chapters provide readers an overview of cutting-edge research in quantum field theories, infinite-dimensional groups, integrable systems, noncommutative geometry, and a wide variety of other areas. Specific topics include:
• Graded structures
• Lie algebra structures
• Quasicrystals
• Sigma models
• Barycentric algebras
• Nijenhuis geometry
Geometric Methods in Physics XLI will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
Contents
Part I: Workshop Lectures.- Chapter 1 Scattering in phase space quantum mechanics - the Born approximation.- Chapter 2 The Schwarzschild's solution and Mach's principle.- Chapter 3 Geometric flows, entropy and nonlinear electrodynamics.- Chapter 4 Weird, Odd, Generalized.- Chapter 5 Restricted orbits of closed range operators.- Chapter 6 On certain Lie algebra structures.- Chapter 7 Darboux transformations applied to graphene in magnetic fields.- Chapter 8 Variants of asymptotics in the Belinski-Khalatnikov-Lifshitz scenario.- Chapter 9 Poisson structures in the Banach setting: comparison of different approaches -2.- Chapter 10 Q-manifolds and sigma models.- Chapter 11 Quasicrystal problem - on rigidity of non-periodic structures from statistical mechanics point of view.- Chapter 12 Qusicrystals in Vernam cipher.- Chapter 13 Explicit Formulae for Deformation Quantization with Separation of Variables of G2,4(C) .- Chapter 14 On the conformal Lie superalgebras K(1; N = 1; 2; 3) and related semi-supersymmetric integrable systems.- Chapter 15 Notes on equivalent formulations of Hamiltonian dynamics on multicotangent bundles.- Chapter 16 Star Product and Star Zeta Function.- Chapter 17 Partitions of unity and barycentric algebras.- Part II: Abstracts of Lectures at "XIII School on Geometry and Physics".- Chapter 18 Nijenhuis Geometry and its Applications.- Chapter 19 Generalized geometry in relation to physics and mechanics -3 .- Chapter 20 Barycentric algebras — convexity and order.
