Singularities and Diffeomorphism - IPAM at UCLA
Explore singularities and diffeomorphism in calculus of variations, covering special cases, classification, and applications in probability and geometry.
Multiscale Inverse Problem, from Schroedinger to Newton to Boltzmann - IPAM at UCLA
Explore multiscale inverse problems across quantum, classical, and statistical physics, connecting Schroedinger, Newton, and Boltzmann equations to reveal universal mathematical principles in diverse scientific domains.
Carlos Pérez- Fractional Poincaré Inequalities for Doubling and Non-Doubling Weights
Explore fractional Poincaré-Sobolev inequalities using Harmonic Analysis, unifying and improving known results for doubling and non-doubling weights in mathematical analysis.
Harmonic Analysis Techniques for -Almost- Minimizers
Explore harmonic analysis techniques for (almost-)minimizers, focusing on free boundary theory and calculus of variations. Learn about applications to geometric measure theory and domain geometry.
A Proposal for Open DT Invariants
Explore open DT invariants, refined invariance, and boundary conditions in moduli spaces with Sergei Gukov. Delve into generating series, topological vertex, and infinite projects in this advanced mathematics lecture.
Functional Inequalities and Improvements: Stability - Part 2
Explore functional inequalities, their optimal constants, and stability properties. Learn strategies for addressing these issues and recent developments in improved inequalities for non-optimizers.
The Man Who Invented Calculus - The Life and Work of Madhava - Lecture 3
Explore Madhava's groundbreaking mathematical contributions, including calculus foundations, infinite series, and abstract approaches, in this lecture by P P Divakaran on the 14th-century Kerala mathematician's life and work.
Laplace Transform of the Unit Step Function - Laplace Transform
Explore the unit step function and its Laplace Transform in this comprehensive video lesson, enhancing your understanding of differential equations and mathematical analysis.
Mathematical Analysis and Numerical Methods for Inverse Scattering Problems
Explore mathematical analysis and numerical methods for inverse scattering problems, covering applications, challenges, algorithms, and recent progress in stability analysis and deep learning approaches.
Rates of Change from Graphs - Calculus Concepts
Explore equations related to rates of change from graphs, including average, estimated, and instantaneous rates. Learn practical applications with an experienced mathematics instructor.
Quantitative Results on the Method of Averaged Projections
Quantitative analysis of averaged projections method in convex optimization, focusing on asymptotic regularity and weak convergence in CAT(0) spaces using proof mining techniques.
Sam Sanders - Uniformity in Mathematics
Explore uniformity in mathematics, from historical examples to modern applications. Examine how uniform theorems challenge traditional logical systems and impact proof methods across various mathematical domains.
Variational and Jump Inequalities
Explore variational and jump norms in mathematical analysis, covering applications in rough paths, singular integrals, and ergodic theory. Gain insights into endpoint results and their proofs.
Alexander Volberg - Poincaré Inequalities on Hamming Cube - Analysis, Combinatorics, Probability
Explore improved L^1-Poincaré inequality constants on Hamming cube, comparing with Gaussian space. Discuss proofs, estimates, and related mathematical concepts in analysis, combinatorics, and probability theory.
Regularity of Free Boundaries in Obstacle Problems - Lecture III
Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
Regularity of Free Boundaries in Obstacle Problems Lecture I
Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.
On Yuansi Chen's Work on the KLS Conjecture III
Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Eldan's Stochastic Localization technique and its implications for the slicing problem.
On Yuansi Chen's Work on the KLS Conjecture I
Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.
Functional Inequalities and Concentration of Measure I
Explore concentration inequalities in probability and geometric analysis, focusing on functional inequalities and their applications to Lipschitz functions in continuous and discrete settings.
Young Towers for Geodesic Flows on Certain Non-Positively Curved Surfaces - ICTP 2021
Explore geodesic flows on non-positively curved surfaces through Young towers, covering history, results, Jacobi fields, and hyperbolic maps with expert Carlos Matheus.
Introduction to Frames and Riesz Bases - Part 1
Explore key concepts of frames and Riesz bases in functional analysis, including characterizations, properties, and applications like Sigma-Delta quantization.