An Introduction to Super Critical Singularities - Lecture 4: Stability of Implosion
Explore advanced concepts in non-linear PDE singularities, focusing on defocusing problems and their connection to fluid mechanics. Gain insights into key results, open problems, and proof techniques.
An Introduction to Super Critical Singularities - Lecture 3: On Self Similar Solutions for Compressible Euler
Explore self-similar solutions for compressible Euler equations and their role in singularity formation for non-linear PDEs, with connections to fluid mechanics.
An Introduction to Super Critical Singularities - Lecture 2: Front Singularities
Explore front singularities in non-linear PDEs, focusing on defocusing problems and their connection to fluid mechanics. Gain insights into key results, open problems, and proof techniques.
An Introduction to Super Critical Singularities - Lecture 1: Energy Super Critical Singularity Formation
Explore energy super critical singularity formation in non-linear PDEs, focusing on recent discoveries in defocusing problems and their connection to fluid mechanics.
Global Solutions to Quadratic Systems of Stochastic Reaction-Diffusion
Explorez les solutions globales des systèmes quadratiques de réaction-diffusion stochastique en dimension deux, avec un accent sur les perturbations à quatre espèces.
Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
Explore particle approximation of the parabolic-parabolic Keller-Segel system in the plane, focusing on stochastic particle systems, tightness, and weak solutions for small sensitivity parameters.
Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities
Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.
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.
Exponential Expression Rates for Neural Operator Approximation to Solution Operators of FBSDEs
Explore exponential expression rates in neural operator approximations for FBSDE solution operators, advancing mathematical finance understanding.
Geometric Aspects of the Planar Least Gradient Problem
Explore geometric aspects of the planar least gradient problem, delving into mathematical concepts and analytical techniques.
Monge-Ampère's Equation in Hypercomplex Geometry
Explore Monge-Ampère's equation in hypercomplex geometry, delving into advanced mathematical concepts and their applications.
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.
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.