Determinants, Commuting Flows, and Recent Progress on Completely Integrable Systems
Explore recent developments in completely integrable nonlinear dispersive PDE, including a priori bounds, orbital stability, well-posedness, and Gibbs distributed initial data dynamics.
Generic Regularity in Obstacle Problems - SIAM PDE Seminar
Explore the generic regularity in obstacle problems with Alessio Figalli. Learn about recent advancements in understanding singular sets and their codimension within free boundaries in elastic membrane equilibrium.
Fluctuation Theory in the Boltzmann-Grad Limit
Explore fluctuation theory in the Boltzmann-Grad limit for hard-sphere gases, examining dynamical correlations and their implications for the kinetic Boltzmann equation and large deviation asymptotics.
The Thresholding Scheme for Mean Curvature Flow and De Giorgi's Ideas for Gradient Flows
Explores the thresholding scheme for mean curvature flow in multi-phase systems, its applications in grain growth, and convergence proofs based on De Giorgi's gradient flow ideas.
Energy Minimization Problems for Liquid Crystals - SIAM PDE Seminar
Explore energy minimization in liquid crystals through probability density, tensor averages, and molecular orientation theories with Sir John Ball.
Multiphase Models of Living Tissues and the Hele-Shaw Limit
Explore multiphase models of living tissues, focusing on mechanical modeling for tissue repair and tumor growth. Discover mathematical analysis techniques and incompressible limit cases in this advanced PDE seminar.
Propagation of Randomness Under the Flow of Nonlinear Dispersive Equations
Explore the propagation of randomness in nonlinear dispersive equations with Andrea R. Nahmod, delving into advanced mathematical concepts and their applications in this insightful lecture.
The Hamilton-Jacobi Equation: Past and Present
Explore the historical and contemporary significance of the Hamilton-Jacobi equation in mathematics with insights from Ryan Hynd of the University of Pennsylvania.
Structure Preservation in the Discretization of Partial Differential Equations
Explore structure preservation techniques in discretizing partial differential equations, enhancing numerical accuracy and stability in computational mathematics.
Differential Operators and the Geometry of Domains in Euclidean Space
Explore the interplay between differential operators and domain geometry in Euclidean space with Tatiana Toro's insightful lecture, the inaugural AMS Maryam Mirzakhani Lecture at JMM 2020.
From Newton to Boltzmann - Fluctuations and Large Deviations in Hard Sphere Gas Dynamics
Explore macroscopic fluctuations in hard sphere gases, including deviations from the Boltzmann equation, central limit theorem, and large deviation bounds in the Boltzmann-Grad limit.
Regularity of Solutions to Elliptic Operators and Elliptic Systems
Explore the mathematical intricacies of elliptic operators and systems, focusing on solution regularity in this advanced lecture by renowned mathematician Jill Pipher.
Seminar in the Analysis and Methods of PDE - Christopher K.R.T. Jones
Explore stability indices for nonlinear waves and patterns in PDEs, focusing on Evans Function and Maslov Index approaches, their geometric interpretations, and recent advancements in complex problem analysis.
Oxford Calculus: How to Solve the Heat Equation
Learn to solve the Heat Equation, a fundamental PDE in calculus, with Oxford mathematician Dr Tom Crawford. Includes practice questions, interactive worksheets, and a free calculator app for comprehensive understanding.
Oxford Calculus - Separable Solutions to PDEs
Learn to solve partial differential equations using separable solutions with Oxford mathematician Dr Tom Crawford. Includes examples, practice worksheets, and links to a free calculator app for checking your work.
Oxford Calculus - Heat Equation Derivation
Comprehensive derivation of the Heat Equation from physical principles, including Liebniz Rule and Fourier's Law. Extends to 2D and 3D applications with interactive exercises for practice.
Variational Bayesian Approximation of Inverse Problems Using Sparse Precision Matrices
Explore Variational Bayes as an efficient alternative to MCMC for solving inverse problems in PDEs, using sparse precision matrices and stochastic optimization for improved computational tractability.
PECANNs - Physics and Equality Constrained Artificial Neural Networks
Innovative approach to physics-informed neural networks using constrained optimization, addressing hyperparameter challenges and improving accuracy for scientific applications involving multi-dimensional PDEs.
Seminar in the Analysis and Methods of PDE - Andrea Bertozzi
Explore the physics behind "tears of wine" phenomenon, examining undercompressive shocks in thin films and their role in the formation of wine tears using mathematical modeling and analysis.
Conservative Adaptive Rank Integrators for Nonlinear Kinetic Models
Explore low-rank time integrators for PDEs, including explicit and implicit schemes, with applications to Vlasov, heat, Fokker-Planck, and advection-diffusion equations.
High-Dimensional PDEs, Tensor Networks, and Convex Optimization
Explore innovative computational methods for high-dimensional PDEs using tensor networks and convex relaxations, addressing the curse of dimensionality with low-order statistics approximations.