Class Timings: 11 am-12:30 pm on Mondays and Tuesdays
First Meeting: 12th January 2021.
Prerequisites: Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics, (all at the level of Landau and Lifshitz), complex analysis, group theory.
Textbooks: There are no fixed textbooks for the course. We will be drawing on many sources from the published literature and the internet.
Structure of the course: The course will cover a number of applications of geometry and topology in the context of physical examples. The emphasis will be on the examples rather than on rigour. This course will be complementary to mathematics courses on geometry and topology.
Exposure to such courses will be helpful, but not a prerequisite to follow the course.
What students will gain from the course: an appreciation of the commonality between different areas of physics; the unifying nature of geometric and topological ideas in physics.
How the course will achieve its goals: We will take specific examples of systems from different areas of physics and analyse them from a geometric perspective. Make connections wherever possible between the different examples. The course will start with simple examples and graduate to more advanced ones. The choice of examples will depend on the feedback I get from the students.
Assessment: Some classes will include a twenty-minute quiz, in which students are asked to answer simple questions related to the class discussion. For example, filling in missing steps in the derivation; consideration of special cases etc. This will be 40% of the assessment. There will also be regular assignments, which the students will have to turn in on time. These will count as 30%. The remaining 30% is for the final exam. It is not presently clear if the pandemic will permit in-person classes. We hope that the situation will improve by Jan 2021. If this does not happen, classes will be conducted online. In this case, students taking the course will be required to have a good internet connection. If you need help in this regard, please contact the ICTS and consult your appointment letter for more details.