Construction of Invariant Measures for 2D Euler and Slow Growth of Sobolev Norms
Explore the growth of Sobolev norms in 2D Euler equations, examining invariant measures and their impact on solution behavior in highly regular spaces.
The Multiple Membrane Problem
Explore the N-membranes problem in mathematics, focusing on equilibrium positions of ordered elastic membranes and their free boundary regularity.
ME3255 - Working on Rocket Problems with Solve_IVP
Explore rocket problem-solving using solve_ivp in Python. Learn to model and analyze rocket dynamics for advanced engineering applications.
The Formulation of the Navier-Stokes Equations on Riemannian Manifolds
Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.
Measuring Convergence of Integration Methods: Heun and Runge-Kutta Comparison - Homework 3
Comparez les taux de convergence des méthodes de Heun et Runge-Kutta pour l'intégration numérique, avec des résultats surprenants.
Perturbations of Periodic Sturm-Liouville Operators
Explore perturbations of periodic Sturm-Liouville operators, focusing on Hill's equation and its applications in crystal physics. Analyze spectral changes under L1-assumptions and finite first moment conditions.
Linear Systems and Differential Equations in Random Matrix Theory
Explore linear systems and differential equations in random matrix theory, focusing on solving nonlinear equations using Hankel operators, Fredholm determinants, and tau functions.
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.
The Non-Abelian p-Curvature Conjecture
Explore a generalized p-curvature conjecture for non-linear ODEs, its implications for algebraic geometry, and proof techniques inspired by Katz and Esnault-Groechenig's work.
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.
Index Theory and Applications to Scalar Curvature
Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.
A Resource Sharing Model with Local Time Interactions
Explore a mathematical model for resource sharing, focusing on local time interactions in financial contexts. Gain insights into advanced mathematical finance concepts.
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.
Differential Equations and Topology in Algebraic Varieties
Explore differential equations and topology, covering algebraic varieties, De Rham cohomology, monodromy, and the Riemann-Hilbert problem in this advanced mathematical lecture.