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.

Autorentext

Dr. Piotr Kielanowski is a professor of theoretical and mathematical physics at the University of Bialystok, 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 Bialowieza 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 Bialystok. Since 2019, she has served as dean of the Faculty of Mathematics at the University of Bialystok. 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 Bialowieza Workshop on Geometric Methods in Physics since 2016.

Dr. Tomasz Golinski is an assistant professor of mathematics at the University of Bialystok, 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.