Geometry and Topology in Physics -Topical (PHY-403.5)

ICTS Course no.: PHY-403.5

Venue: Online

Class timings: 11:00-12:30 Mondays and 04:00- 05:30 Tuesdays

First meeting: 11:00 am, 10th January 2022

Course description: 

Prerequisites: Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics, (all at the level of Landau and Lifshitz), complex analysis, some basic knowledge of 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. We will draw on standard texts like Nakahara and Nash and Sen for some parts of the course. We will also have student reviews of important papers towards the end of the course.

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. An opportunity to develop and hone their presentation skills in a friendly environment. 

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: Assessments will be based on assignments (50%) and term paper presentations (50%) by the students. Students have to choose from a list of classic papers (one paper per student) and make a presentation to the class.  

It is not presently clear if the pandemic will permit in-person classes. We hope that the situation will improve. 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.