Related Rate Problems in AP Calculus
Learn strategies for solving related rate problems, including soap bubbles, cylindrical tanks, right triangles, conical tanks, and street light scenarios using similar triangles.
Statistical Inverse Problems and PDEs: Progress and Challenges
Explore statistical inverse problems and PDEs, covering Bayesian approaches, computational challenges, and mathematical guarantees for algorithms in high-dimensional settings.
Solving Systems of ODEs via Combinatorial Homological Algebra
Exploring efficient computation of homological representations in dynamical systems, with applications to differential equations and parameter space analysis.
Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids
Explores semi-Lagrangian discretisation of Monge-Ampère operator on P1 finite element spaces, discussing challenges and solutions for numerical methods in solving Monge-Ampère equations, with applications in inverse reflector problems.
Axel Målqvist - Localization of Multiscale Problems
Explore multiscale problem-solving techniques, focusing on Local Orthogonal Decomposition for PDEs. Learn about convergence, high-contrast data, and applications to time-dependent problems.
Solving the 4NLS with White Noise Initial Data
Explore white noise initial data in solving 4NLS, covering Hamiltonian PDE, globalization arguments, and limit equations. Gain insights into complex mathematical concepts and proofs.
A Controllability Approach to SDEs Driven by Degenerate Noises and Applications to Networks of Oscillators
Explore stochastic differential equations with degenerate noise, focusing on controllability and applications to oscillator networks. Gain insights into exponential mixing and solid controllability.
Entropy Method for Hypocoercive BGK and Fokker-Planck Equations
Explore entropy methods for hypocoercive equations, focusing on BGK and Fokker-Planck models. Learn about decay rates, auxiliary functionals, and regularization techniques in non-symmetric systems.
Phase-Field Models for Motion by Mean Curvature - Lecture 2
Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.
Uncertainty Quantification for Kinetic Equations I
Overview of uncertainty quantification for kinetic equations, covering Monte Carlo methods, multi-fidelity techniques, and stochastic Galerkin particle methods. Explores computational challenges and recent advancements in the field.
Antonio Esposito: Nonlinear Degenerate Cross Diffusion Systems with Nonlocal Interaction
Explores nonlinear degenerate cross-diffusion systems with nonlocal interaction, proving global existence of weak solutions using a semi-implicit JKO scheme for applications in social sciences, finance, and biology.
Regularity of Free Boundaries in Obstacle Problems - Lecture III
Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
Regularity of Free Boundaries in Obstacle Problems Lecture I
Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.
On Yuansi Chen's Work on the KLS Conjecture III
Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Eldan's Stochastic Localization technique and its implications for the slicing problem.
On Yuansi Chen's Work on the KLS Conjecture I
Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.
Panorama of Mathematics - Alfio Quarteroni
Explore reduced order models for solving partial differential equations, focusing on complexity reduction and efficient simulations in multiphysics problems.
Differential Equations and Mixed Hodge Structures
Explore the interplay between differential equations and mixed Hodge structures, focusing on periods, kappa series, and motific gamma in number theory and algebraic geometry.
Hilbert's 16th Problem and O-Minimality - Lecture 1
Explore the topology of cycles, limit cycles, and related mathematical concepts in this advanced graduate-level lecture on Hilbert's 16th problem and o-minimality.
Harmonic Maps Between Surfaces and Teichmüller Theory - Lecture 1
Explore harmonic maps between surfaces, their applications, and connections to Teichmüller theory in this advanced lecture on geometric analysis and complex geometry.
Sums of Squares and Applications to Hypoellipticity
Explore sums of squares in differential equations, focusing on hypoellipticity. Learn about key theorems, counterexamples, and applications in this advanced mathematics lecture.
Linearized Instability for Neutral Functional Differential Equations with State-Dependent Delays
Lecture on linearized instability for neutral functional differential equations with state-dependent delays, presenting recent research findings in advanced mathematics.