The Isoperimetric Problem in Cubes and Torii
Explore the isoperimetric problem in cubes and torii, delving into geometric principles and mathematical concepts with Federico Glaudo's insightful analysis.
Symmetries, Conservation Laws and Variational Principles - Part III
Explore symmetries, conservation laws, and variational principles in mathematics, focusing on Noether Theorems and their applications in various geometric structures and physical systems.
Symmetries, Conservation Laws and Variational Principles - Part II
Explore advanced mathematics of Noether Theorems in calculus of variations, covering symmetries, conservation laws, and variational principles. Gain insights into differential geometric structures and their applications.
Symmetries, Conservation Laws and Variational Principles
Explore symmetries, conservation laws, and variational principles in mathematics, focusing on Noether Theorems and their applications in calculus of variations and differential geometry.
Generic Regularity in Obstacle Problems
Explore the classical obstacle problem, its free boundary, and recent developments in regularity theory with insights from renowned mathematician Alessio Figalli.
Geometric Aspects of the Planar Least Gradient Problem
Explore geometric aspects of the planar least gradient problem, delving into mathematical concepts and analytical techniques.
Riesz Inequality for Polygons: Symmetry and Symmetry Breaking
Explore counterparts of Hardy-Littlewood and Riesz inequalities for polygons, examining symmetry and symmetry breaking in nonlocal isoperimetric problems.
Eigenvalues and Minimal Surfaces
Explore Laplace operator eigenvalues, their physical significance, and connection to minimal surfaces. Discover recent findings in isoperimetric eigenvalue problems for Riemannian surfaces.
Optimal Immersions in the Calculus of Variations of Surfaces
Explore innovative minmax techniques for optimal surface immersions, including recent progress on Yau, Willmore, and 16π conjectures in calculus of variations.
Regularity for Stationary Varifolds
Explore advanced concepts in geometric measure theory, focusing on regularity properties of stationary varifolds and their applications in minimal surface theory.
Dissipation and Mixing: From Turbulent Flows to Weak Solutions - Lecture 1
Explore dissipation and mixing in turbulent flows, focusing on weak solutions in hydrodynamics. Gain insights into anomalous dissipation and recent developments in mathematical fluid mechanics.
Solving the Brachistochrone Problem with Random Numbers
Discover the fastest path for a frictionless bead using random numbers to solve the Brachistochrone problem in physics.
Review of Lagrangian Mechanics with Examples - Projectile Motion and Driven Spring Oscillation
Explore Lagrangian mechanics through projectile motion and driven spring oscillation examples, including numerical calculations and Python implementation.
C^0 Convex Integration for Incompressible Euler - Lecture 4
Explore C^0 convex integration for incompressible Euler equations, focusing on a novel iteration method producing continuous solutions, drawing parallels with Nash's theorem from Lecture 3.
The Brownian Transport Map - IPAM at UCLA
Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.
Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2
Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.
A Variational Principle of Minimum for Navier-Stokes Equation Based on the Symplectic Formalism
Explore a variational principle of minimum for Navier-Stokes equations using symplectic formalism, advancing understanding of fluid dynamics and mathematical physics.
Patterns in Tri-Block Copolymers: Droplets, Double-Bubbles and Core-Shells - A New Partitioning Problem
Explore patterns in tri-block copolymers, including droplets, double-bubbles, and core-shells. Examine a novel partitioning problem in mathematical physics and materials science.
Variational Principles in Physics - Standard Prejudices and Paradoxes
Explore variational principles in physics, challenging standard assumptions and uncovering paradoxes with Professor Jerzy Kijowski's insightful seminar.
The Onsager Theorem and Beyond - Lecture Series
Explore advanced topics in fluid dynamics and differential geometry with renowned mathematician Camillo De Lellis, covering Onsager's theorem, Euler equations, and isometric embeddings.
Classical Mechanics - Introduction to Lagrangian Mechanics
Explore the fundamental principles of Lagrangian mechanics, a powerful mathematical framework for analyzing physical systems and understanding classical mechanics.