Lectures related to Optimal Transport: In-Depth Evaluation

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Variational Formulation: Information Measures

Explores variational formulation for measuring information content and divergence between probability distributions.

Information Measures: Entropy and Information Theory

Explains how entropy measures uncertainty in a system based on possible outcomes.

Maximum Principle in Heat Equation

Explores the maximum principle in the context of the heat equation and the concept of the cylinder.

Heat Equation: Separation of Variables

Covers the application of separation of variables method to solve the heat equation.

Entropy and the Second Law of Thermodynamics

Covers entropy, its definition, and its implications in thermodynamics.

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Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Harmonic Forms: Main Theorem

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

Diffusion Equation

Covers the Fourier law, heat equation, Righi-Leduc effect, and related experiments.

Heat Transfer: Equilibrium Approach and Thermodynamic Potentials

Reviews heat transfer mechanisms, entropy, and thermodynamic potentials in relation to equilibrium and Carnot cycles.

Thermal Transfer Fundamentals

Explores thermal transfer principles, including laws of thermodynamics, heat mechanisms, and Fourier's equation.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Thermodynamics: Entropy and Ideal Gases

Explores entropy, ideal gases, and TDS equations in thermodynamics, emphasizing the importance of the Clausius inequality and the Carnot cycle.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Heat Equation: Stationary Distribution

Explores the heat equation, equilibrium equations, heat flux, and harmonic functions in heat distribution.

Thermal Diffusion: Basics and Applications

Explores thermal diffusion, specific heat, conductivity, and expansion in materials, explaining how energy is transferred between atoms and molecules.

Correlations of the Liouville function

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