In various physical applications we often encounter notions coming from geometry and topology. Basic examples of such setups include among others: Aharonov-Bohm effect, Berry phase, Magnetic monopoles, general notions of symmetry and charge, Electrodynamics and gauge theories more generally, General relativity, Geometry of the phase space in analytical mechanics, quantum anomalies and topological phases of matter: and many many more. Typically such concepts in Physics classes are treated ad hoc. {\it The main goal of this class is to develop the rather simple but beautiful mathematical language in which all of these phenomena can be naturally phrased and discussed.} This course is not in physics and not in mathematics. It is rather a course in mathematical methods for physics. We will study relevant aspects from various subfields of mathematics with the main thread being geometry and topology. The desired learning outcome of this class is that the students will understand the basic notions listed in the syllabus, identify them in physical contexts, and ultimately be able to use geometrical and topological reasoning in physical applications. The class is suitable for all graduate students and strong$+$motivated undergraduate students possessing the relevant background knowledge.
- Teacher: שלמה רזמט