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.
Dr. Piotr Kielanowski is a professor of theoretical and mathematical physics at the University of Białystok,
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 Białowieża 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 Białystok. Since
2019, she has served as dean of the Faculty of Mathematics at the University of Białystok. 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 Białowieża Workshop on Geometric
Methods in Physics since 2016.
Dr. Tomasz Goliński is an assistant professor of mathematics at the University of Białystok,
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.
