Geometric Methods In Mathematical Physics

AY2024/2025 Semester 1

This course is an introduction to the mathematical structures which underlie the description of physical systems, with a special emphasis on geometric concepts. You will acquire basic notions on manifolds, differential forms, curvatures, Lie groups, symmetries. You will also learn about the direct use of these concepts for the description of various physical phenomena and for the construction of a geometrically consistent formulation of Lagrangian and Hamiltonian systems. The understanding of such concepts leads to crucial insight into topics ranging from electromagnetism and quantum mechanics to plasmas physics and general relativity. Both the mathematical and intuitive understanding of the introduced objects will be emphasized. This course is relevant for mathematics and physics students interested to later work in areas such as robotics, quantum computing, electromagnetic and acoustic sensing, control and learning. Students who want to pursue ostgraduate degrees in pure or applied mathematics and theoretical physics will find this course relevant.