Monge-Ampère's Equation in Hypercomplex Geometry
Explore Monge-Ampère's equation in hypercomplex geometry, delving into advanced mathematical concepts and their applications.
Mathematics of Stem Cells: Mechanistic Mathematical Modelling vs Single Cell Data Analysis
Explore mathematical approaches to stem cell research, comparing mechanistic modeling with single cell data analysis techniques.
A Gentle Introduction to Hardy Spaces
Explore Hardy spaces through a gentle introduction, covering fundamental concepts and applications in complex analysis and functional theory.
Free Boundary Minimal Annuli Immersed in the 3-Ball
Explore free boundary minimal annuli in the 3-ball, focusing on construction methods, Steklov eigenvalues, and perturbation techniques for exact free boundary minimality.
Unique Continuation for Solutions of Discrete and Continuous Elliptic Partial Differential Equations
Explore unique continuation properties for elliptic equation solutions, including discrete harmonic functions and the Landis conjecture, with applications to Anderson localization.
Maximization of Neumann Eigenvalues under Diameter Constraint
Explore Neumann eigenvalue maximization under diameter constraints, delving into advanced spectral geometry concepts and mathematical analysis techniques.
Third-Order Eigenvalue Problems
Explore third-order eigenvalue problems with Maria Del Mar Gonzalez, delving into advanced mathematical concepts and their applications in spectral geometry.
Aggregation-Diffusion and Kinetic PDEs for Collective Behavior: Applications in Sciences
Explorez les modèles mathématiques de comportement collectif, leurs propriétés et applications en biologie et ingénierie. Découvrez les phénomènes de ségrégation, transitions de phase et consensus.
On the Critical Points of Steklov Eigenfunctions
Explore critical points of Steklov eigenfunctions on Riemannian manifolds, examining relationships between eigenfunction indexes, boundary behavior, and Euler characteristics.
An Overdetermined Eigenvalue Problem and the Critical Catenoid Conjecture
Explore an overdetermined eigenvalue problem on the two-sphere and its implications for characterizing the critical catenoid as a unique embedded free boundary minimal annulus.
Weyl Asymptotics for Poincare-Steklov Eigenvalues in Domains with Lipschitz Boundaries
Explorez les asymptotiques de Weyl pour les valeurs propres de Poincaré-Steklov dans un domaine à frontière lipschitzienne, avec une approche basée sur l'approximation par des problèmes réguliers.
Spectral Minimal Partitions of Metric Graphs: What and Why
Explorez les partitions minimales spectrales des graphes métriques, leurs liens avec la théorie spectrale et les coupures de Cheeger, et découvrez de nouveaux résultats sur les graphes non bornés et les conditions de Robin.
Curvature Positivity and $\bar\partial$ Equation with Optimal $L^2$ Estimate - ICBS 2024
Explore recent advancements in multiplier ideal sheaves, multiplier submodule sheaves, and converse L^2 theory. Gain insights into Nakano semipositivity criteria and solutions to Lempert's problem.
Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications
Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.
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.
On Strong Solutions of Time Inhomogeneous Itô's Equations with Morrey Diffusion Gradient and Drift - CSMQ Colloquium
Explore strong solutions of time-dependent Itô's equations with irregular diffusion and drift terms in Morrey spaces, including existence, uniqueness, and related parabolic equations.
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.
The Method of Gauge Transform II
Explorez la méthode de transformation de jauge et son application aux problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski.
The Method of Gauge Transform - Lecture 4
Explorez la méthode de transformation de jauge et ses applications dans les problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski de l'University College London.