This lecture is devoted to Noether’s theorems and the study of the interplay between symmetries and conservation laws, from ordinary mechanics to general relativity. In order to start on a common ground and interest a broad audience, we will begin with a review of Noether’s (first) theorem in ordinary non-relativistic mechanics. This will enable us to settle some subtleties, agree on...
Two of the most beautiful examples of the interaction between mathematics and physics involve knot theory and mirror symmetry. In this talk, I will describe a new connection between them. The solution to a central problem in knot theory, the knot categorification problem, comes from a new application of mirror symmetry.
Interacting quantum particles can form non-trivial states of matter characterized by topological order, which features several unconventional properties such as topological degeneracy and fractionalized quasiparticles. In addition, it also provides a promising platform for realizing quantum computing in a robust manner. In this series of lectures, I will introduce the basics of topological...
These lectures will cover the concepts and techniques of effective field theory. I will try to introduce several of the useful techniques which do not usually get covered in the standard QFT courses and books. We will start with the effective field theory aspects of QED, and end with the treatment of general relativity as a quantum field theory using effective field theory techniques.
Translational tiling is a covering of a space (e.g., Euclidean space) using translated copies of a building block, called a "tile'', without any positive measure overlaps. What are the possible ways that a space can be tiled?
One of the most well known conjectures in this area is the periodic tiling conjecture. It asserts that any tile of Euclidean space can tile the space periodically. This...
