Lectures related to Hamiltonian Homeomorphisms on Surfaces

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Group Theory Fundamentals

Introduces group theory basics and group action concepts with associated subsets.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Symmetries in Physics

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.