This volume collects papers based on lectures given at the XLI Workshop on Geometric Methods in Physics, held in Bialystok, 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.
Part I: Workshop Lectures.
Chapter 1 Scattering in phase space quantum
mechanics the Born approximation.
Chapter 2 The Schwarzschilds solution
and Machs 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.
Dr. Piotr Kielanowski is a professor of theoretical and mathematical physics at the University of Biaystok, Poland and during the period 1995-2023 he was a professor at the Center for Research and Advanced Studies of the Polytechnic University of Mexico in Mexico City (Centro de Investigación y de Estudios Avanzados). He has published more than 80 original papers in the field of particle phenomenology and has mentored several PhD students. He is co-author of a book on quantum mechanics (Arno Bohm, Piotr Kielanowski, G. Bruce Mainland, Quantum Physics States, Observables and Their Time Evolution, Springer 2019, ISBN: 978-94-024- 1760-9). He has been a member of the Organizing Committee of the Biaowiea Workshop on Geometric Methods in Physics for about 20 years and has been the editor of successive volumes of the proceedings.
Alina Dobrogowska is an associate professor of mathematics at the University of Biaystok. Since 2019, she has served as dean of the Faculty of Mathematics at the University of Biaystok. Her scientific interests focus on topics such as: factorization method, orthogonal polynomials, integrable systems, bi-Hamiltonian structures, Poisson geometry, Lie algebras and Lie algebroids. She has published around 40 original papers. She is also a coauthor of the book 40 Years of Workshop on Geometric Methods in Physics. She has been the member of the Organizing Committee of the Workshop on Geometric Methods in Physics since 2001 and has been the editor of recent volumes of the proceedings.
Dr. David Fernández is a professor of theoretical physics at the Center for Research and Advanced Studies of the National Polytechnic Institute in Mexico City. He has published more than 80 original papers in the field of mathematical physics and has mentored 14 PhD students. He has made important contributions in the generation of exactly solvable Hamiltonians through the factorization method and supersymmetric quantum mechanics. He has been a member of the Advisory Committee of the Biaowiea Workshop on Geometric Methods in Physics since 2016.
Dr. Tomasz Goliski is an assistant professor of mathematics at the University of Biaystok, Poland. He has published around 20 original papers in the field of integrable systems and infinitedimensional geometry. He has been the scientific secretary of the Workshop on Geometric Methods in Physics since 2003 and has been the editor of recent volumes of the proceedings. He is also a coauthor of the volume 40 Years of Workshop on Geometric Methods in Physics.
