Lectures related to Polish space

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Optimal Transport: Disintegration Theorem

Covers the Disintegration Theorem in the context of Optimal Transport.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Preliminaries in Measure Theory

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Convergence and Completeness

Covers convergence, completeness, and properties of metric spaces and Banach spaces.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Wedge: Family of Spaces

Explores the concept of a wedge of spaces and explicit parainization.

Lipschitz Maps and Compact Domains

Covers Lipschitz maps, compact domains, changing variables, counting problems, and probability of ideals.

Metric spaces: topology

Covers metric spaces and topology, exploring properties of metrics, open/closed sets, and boundaries.

Functional Analysis I: Foundations and Applications

Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Functional Analysis I: Consequences of Baire Theorem

Explores the implications of Baire Theorem in functional analysis and metric spaces.

The Banach Fixed Point Theorem

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Optimal Transport: Regularity and Brenier's Theorem

Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.

Hilbert Space: Geometry, Bases

Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.

Functional Analysis: Baire's Theorem

Covers the proof of Baire's Theorem, consequences of the Baire Category Theorem, and the principle of uniform boundedness.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Fourier Transform and Schwartz Space

Explores the Fourier transform, Schwartz space, and Riemann-Lebesgue lemma in quantum physics.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.