Wave Localization and the Landscape Law
Explore wave localization in complex media, introducing the landscape concept for predicting eigenfunctions, decay patterns, and eigenvalues. Discover new insights on Schrödinger operators and quantum observables.
Introduction to Theory and Numerics of Partial Differential Equations - Lecture 4
Explore advanced concepts in partial differential equations, focusing on theory and numerical methods for solving complex mathematical problems in physics and engineering.
Global Solutions for Singular SPDEs
Explore groundbreaking research on global solutions for singular stochastic partial differential equations with renowned mathematician Martin Hairer from Imperial College London.
Connections Between Geometry and Partial Differential Equations
Explore the fascinating interplay between geometric structures and partial differential equations, uncovering deep mathematical insights and applications.
Boundary Regularity of Minimal Surfaces
Explore boundary regularity of minimal surfaces with Camillo De Lellis. Gain insights into advanced mathematical concepts and their applications in geometric analysis.
Poseidon: Efficient Foundation Models for PDEs - Tutorial 1
Explore efficient foundation models for PDEs with Poseidon, focusing on innovative techniques and applications in computational science.
On the Regularity Implied by the Assumptions of Geometry
Explore the theory of Regularity Transformation equations and their impact on non-regular spacetime geometry, including applications in General Relativity and Einstein-Euler equations.
Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization
Explore sample size estimates for risk-neutral semilinear PDE-constrained optimization using SAA approach, covering nonasymptotic analysis and numerical illustrations.
Nonmonotone Forward-Backward Splitting Method for Infinite-Dimensional Optimization Problems
Explore nonmonotone forward-backward splitting for nonsmooth composite problems in Hilbert spaces, covering convergence analysis, complexity, and numerical experiments.
Looking for p-Energy Forms in Cheeger Spaces
Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.
Numerical Approaches to Modelling Curved Surfaces
Explore numerical methods for modeling curved surfaces, focusing on applications in physics and biology.
Global Well-Posedness and Scattering for the Conformal Nonlinear Wave Equation
Explore global well-posedness and scattering in conformal nonlinear wave equations with Benjamin Dodson's in-depth mathematical analysis.
The Korteweg-de Vries Hierarchy in Rough Function Spaces
Explore the Korteweg-de Vries hierarchy in rough function spaces, focusing on wellposedness and the Miura map's role in translating to the Gardner hierarchy.
Finite Point Blowup for the Critical Generalized Korteweg-de Vries Equation
Explore finite point blowup in critical generalized KdV equations, uncovering new blow-up dynamics and rates. Gain insights into recent advancements in nonlinear wave theory.
Microlocal Methods for Operators with Analytic Coefficients - Lecture 4
Explore advanced microlocal methods for operators with analytic coefficients in this in-depth mathematical lecture by Maciej Zworski.
Microlocal Methods for Operators with Analytic Coefficients - Lecture 3
Explore advanced microlocal methods for operators with analytic coefficients in this in-depth mathematical analysis lecture by Maciej Zworski.
Microlocal Methods for Operators with Analytic Coefficients - Lecture 2
Explore advanced microlocal methods for operators with analytic coefficients in mathematical physics and spectral theory.
Microlocal Methods for Operators with Analytic Coefficients - Lecture 1
Explore microlocal methods for operators with analytic coefficients in this advanced mathematics lecture by Maciej Zworski.
Nonlinear Hyperbolic Conservation Laws on Manifolds
Explore nonlinear scalar hyperbolic equations on Riemannian varieties, covering existence, uniqueness, entropy conditions, finite-volume schemes, and numerical results.
Finite Difference Schemes for Partial Differential Equations in Oceanography - Munk Equation and Shallow Water Equations
Explore high-order finite difference schemes for Munk equation and Shallow Water equations on Cubed Sphere grid, with numerical and convergence analysis.
A New Approach to the Hot Spots Conjecture
Explore a novel approach to the hot spots conjecture in mathematics, focusing on eigenvalues of Neumann and Dirichlet Laplacians and recent advances in the field.