Geometric Methods in Physics XLII: Workshop, Białystok, Poland, 2025

This volume collects papers based on lectures given at the XLII Workshop on Geometric Methods in Physics, held in Białystok, Poland in June-July 2025. 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: Twisted Araki–Woods Algebras Monoidal actions in Lie-algebraic context Introductory course to quantum formalism in low dimensions Gelfand triplets in Quantum Mechanics Riemann Hypothesis in terms of the continuous Newton flow Geometric Methods in Physics XLII are a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.