This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Bialystok, Poland in June 2022. These chapters provide readers an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas. Specific topics include:

• Classical and quantum field theories
• Infinite-dimensional groups
• Integrable systems
• Lie groupoids and Lie algebroids

• Representation theoryGeometric Methods in Physics XXXIX 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 Center for Research and Advanced Studies of the Polytechnic University of Mexico in Mexico City. He has published more than 80 original papers in the field of particle phenomenology and has mentored several PhD students. He is the co-author of a book on quantum mechanics (Quantum Physics: States, Observables and Their Time Evolution, Springer, 2019). 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.

Dr. Alina Dobrogowska is a professor in the Faculty of Mathematics of the University of Bialystok, Poland. She has published numerous papers on integrable systems, particularly in relation to factorization methods, bihamiltonian systems, q-difference equations and Lie algebroids. She has been a member of the Organizing Committee of the Workshopsince 2001, and since last year she is the chairman of the Organizing Committee.

Dr. Gerald A. Goldin is a distinguished professor of mathematics, physics, and mathematics education at Rutgers University in New Brunswick, New Jersey. His work in mathematical physics focuses on local current algebras and their representations, measures on infinite-dimensional configuration spaces, quantum vortex configurations, nonlinear electrodynamics, and nonlinear variations of quantum mechanics. With colleagues at Los Alamos National Laboratory, he was an early co-discoverer of the possibility of "anyon" and "nonabelian anyon" statistics. He is a recipient of the Alexander von Humboldt Research Prize in physics, and has been a Workshop participant for over 30 years.

Dr. Tomasz Golinski is an assistant professor in the Faculty of Mathematics of the University of Bialystok, Poland. His research interests address various aspects of mathematical physics, with emphasis on topics related to problems of functional analysis and operator algebras. These include infinite dimensional geometry with emphasis on Poisson geometry on Banach manifolds, Banach Lie groupoids and algebroids, integrable systems, and factorization methods in their discrete version. He has been Secretary of the Workshop since 2003.