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.