An introduction to anyons and Chern Simons theories

Prerequisites: Basic knowledge of quantum mechanics, statistical mechanics, second quantisation.

Topics : (a) Overview, basic ideas of fractional statistics and braiding, general models of anyons, including Fibonacci model, fusion and braiding rules, F and R matrices, quantum dimension, explicit computation for Fibonacci and other models, anyon diagramatics, computing with anyons, single and two qubit gates, quantum error correction, toric code model, X and Z errors, toric code model as an anyon model, S and T matrices, knot invariants, linking numbers, Chern-Simons theories, topological quantum field theories

References

  • Book : Topological quantum : Steve Simon
  • Lecture notes by John Preskill
  • Lecture notes by von Oppen, Peng and Pientka
  • Review articles by Sumathi Rao
  • Other reviews and lecture notes to be specified later

Credit Score: 4

Problem Solving Techniques in Analysis

Timings: All Tuesdays 09:00 AM to 11:00 AM 

Syllabus: The course will focus on solving problem and writing of solutions in Analysis from topics covered in the core courses C1(Analysis 1) and C6 (complex Analysis).

Course outcomes: Student will develop skills in logical deduction, problem solving, and writing mathematics precisely.

First meeting: 12 May 2025

References (from): 
1) Principle of Mathematical Analysis by Rudin
2) Visual Complex Analysis by Tristan Needham


Credit Score: 4