Lectures related to Homogeneous space

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Discusses the AdS/CFT correspondence and its implications for Large N CFT.

Introduces Markov chains, covering basics, generation algorithms, and applications in random walks and Poisson processes.

The Two-Holed Torus

Covers the construction of the connected sum of two tori in 10 minutes.

Discrete-Time Markov Chains: Definitions

Covers the definitions and state probabilities of discrete-time Markov chains.

Discrete-Time Markov Chains: Definitions

Covers the definitions and state probabilities of discrete-time Markov chains.

Homogeneous and Non-Homogeneous Systems

Explores homogeneous and non-homogeneous systems of linear equations, focusing on solution structures.

Higher Homotopy Groups: Generalization and Structure

Explores the generalization and structure of higher homotopy groups, including their abelianness, historical context, and properties of H spaces.

Quotient Groups and Push-outs

Covers the construction of push-outs in the category Ens and philosophical concepts of universality and co-universality.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Homogeneous Spaces and Quotients

Covers homogeneous spaces, group actions, and separating quotient spaces in mathematics.

Linear Systems Solutions

Explores linear systems solutions, including independence of vectors and unique solution conditions.

Kinematic Quantities and Linear Mass Density

Discusses kinematic quantities and linear mass density in examples of metal wires.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Dynamics on homogeneous spaces and interactions with number theory

Explores dynamics on homogeneous spaces, Khintchine theorem, Sullivan's logarithm law, and interactions with number theory.

Catalysis: Hydrogenation

Covers the topic of catalysis, focusing on the process of hydrogenation and the advantages of using soluble catalysts.

Linear Homogeneous Equations

Covers second-order linear homogeneous differential equations and their solutions.

Norm Equivalence and Inverse Inequality

Explores norm equivalence, inverse inequality, and error analysis in finite element methods.

Center of Gravity: Theory and Applications

Explores the theory and applications of the center of gravity in physics, including the calculation of moments, couple forces, and mechanical advantage in levers.