Stability of Sobolev Inequalities - ICBS 2024
Explore quantitative stability of Sobolev inequalities, focusing on Struwe's decomposition and recent advancements in dimensional-dependent estimates for multiple bubbles in various dimensions.
Entropy Analysis and Singularities of Solutions for Nonlinear Hyperbolic Conservation Laws
Explore entropy analysis and singularities in nonlinear hyperbolic conservation laws. Gain insights into open problems, minimal entropy conditions, and phenomena like cavitation and concentration.
Nonlocal Diffusion Model with Dirichlet Boundary Condition - ICBS 2024
Explore nonlocal diffusion models for Poisson equation, focusing on approaches to approximate Dirichlet boundary conditions and analyzing wellposedness and convergence.
Critical Well-Posedness for the Derivative Nonlinear Schrödinger Equation on the Line
Explore critical well-posedness for the derivative nonlinear Schrödinger equation on the line, focusing on recent advancements in resolving the problem in critical space.
Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds
Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
The Ricci Flow - Lecture by Richard Hamilton
Explore the Ricci flow equation, its applications in geometry, and its role in understanding manifold curvature evolution. Gain insights into singularities and geometric analysis.
Hyperbolic and Mixed-Type Problems in Gas Dynamics and Geometry
Explore hyperbolic and mixed-type PDEs in gas dynamics and geometry, focusing on transonic flows and isometric embedding.
Partial Differential Equations and Convexity
Explore elliptic PDEs, convexity preservation, and surprising cases of convexity breaking in evolution equations like porous medium and Stefan problem.
Optimal Estimates for Neumann Eigenvalues
Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.
Maxwell Eigensolvers with Overlapping Schwarz Methods - ICBS 2024
Explore advanced overlapping Schwarz methods for Maxwell eigensolvers, including improved condition number bounds and a novel two-level preconditioned Helmholtz subspace iterative method for edge element approximations.
Recent Topics on Hyperbolic Relaxation Problems
Explore recent advancements in hyperbolic relaxation problems, covering dissipativeness, modeling, boundary conditions, and control in moment closure systems.
Second Order Interior Estimates of Monge-Ampere Type Equations
Explore interior second order derivative estimates for Monge-Ampere type equations, focusing on partial structure cases using Pogorelov estimates and Legendre transforms.
Particle and Game Theoretic Methods for Multi-scale and High Dimensional Problems
Explore Lagrangian and game theoretic approaches for solving complex PDEs, including front speed computation, high-dimensional entropy production, and turbulent combustion analysis.
MAgNet: Mesh Agnostic Neural PDE Solver
Explore innovative neural PDE solver for accurate, scalable climate predictions. Learn about mesh-agnostic architecture combining Implicit Neural Representations and Graph Neural Networks.
Uniform Bounds for Multilinear Singular Integrals - Part 1
Explore uniform bounds for multilinear singular integrals with Olli Saari, delving into advanced mathematical concepts and their applications in analysis.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 3
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 4
Explore Bourgain's groundbreaking proof of the circular maximal function theorem in this advanced mathematical lecture by Jonathan Hickman.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 2
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 1
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into its mathematical intricacies and significance in harmonic analysis.
Sharp Restriction Theory - Part 3
Explore advanced concepts in sharp restriction theory, delving into complex mathematical principles and their applications in functional analysis.
Sharp Restriction Theory - Part 2
Explore advanced concepts in sharp restriction theory, delving into mathematical intricacies and applications with expert guidance from Diogo Oliveira e Silva.