Lectures related to Hamilton-Jacobi Equation: Exact Fields

Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Peierls argument

Explores the Peierls argument and its application in the Ising Model.

Hamiltonian dynamics on convex polytopes

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

Proof of Convergence Rate Theorem

Covers the proof of the convergence rate theorem, emphasizing the correction of a missing factor sqrt{pi_j} in the proof.

Bases in Known Dimension Space

Discusses bases in vector spaces of known dimension and how to determine if a given set is a base.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.