DescriptionMost familiar theories in physics depend on the metric on spacetime: there is a way for observers to say if two points are close or far apart, for example by shining light from one point to the other, and waiting for the reflection to reach back to the original point. Topological field theories, on the other hand, are less familiar quantum field theories that do not depend on the metric on space. They are in many ways simpler, and are often easier to understand mathematically than full quantum field theories. Their study has given rise to a number of important advances in mathematics, such as Witten's results on the Jones polynomial for knots, or the formulation by Kontsevich of homological mirror symmetry for Calabi-Yau varieties. These theories are not only important mathematically, but they are becoming increasingly important in modern physics, with applications ranging from condensed matter to formal string theory. In this project we will study the basics of topological field theories. Pre-requisites and co-requisitesYou should have taken Mathematical Physics II on the second year, Topology III on the third year, and you should be taking either Riemmanian Geometry IV, Advanced Quantum Theory IV or General Relativity IV on the fourth year. If you don't fulfill these requisites but are still interested please talk to us.Reading material
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