Lectures related to Joint Equidistribution of CM Points

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Explores limiting distribution in Markov chains and the implications of ergodicity and aperiodicity on stationary distributions.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

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

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Explores optimal transport in heat equations and metric spaces.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Covers weak derivatives, their properties, and applications in functional analysis.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.