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.
Immunology for Mathematicians
Explore mathematical approaches to immunology, including modeling immune responses and viral dynamics, in this lecture by renowned researcher Alan S. Perelson from Los Alamos National Laboratory.
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.
Flows of Nonsmooth Vector Fields - Lecture 1
Explore the intricacies of non-smooth vector field flows in this advanced mathematics lecture by Camillo De Lellis, delving into complex theoretical concepts and their applications.
An Invitation to Periodicity
Explore the concept of periodicity in mathematics, its applications, and significance across various fields with expert insights from Gaston Mandata N'Guerekata.
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.
Oxford Calculus - Separation of Variables Integration Technique Explained with Examples
Learn to solve first order separable differential equations using the separation of variables method, with worked examples and practice exercises from an Oxford mathematician.
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.
Efficient Quantum Algorithms for Linear and Non-Linear Differential Equations
Explore quantum algorithms for solving differential equations, focusing on efficiency and applications in scientific computation.
Sequential Change-point Detection in Stochastic Differential Equations
Explore advanced techniques for detecting change-points in stochastic differential equations, focusing on sequential methods and their applications in statistical analysis.
Solving a Differential Equation from the Putnam Exam
Explore a challenging differential equation from the renowned Putnam exam, delving into advanced mathematical concepts and problem-solving techniques.
Deep Solver for Jumps in Backward Stochastic Differential Equations - Lecture
Innovative extension of deep solver for FBSDEs with jumps, using neural networks to tackle high-dimensional problems in option pricing and counterparty credit risk.
A Very Interesting Differential Equation
Explore an intriguing differential equation, delving into its unique properties and solution methods for a deeper understanding of mathematical concepts.
Frobenius Structure and p-adic Zeta Function
Explore p-adic Frobenius structures in differential equations, their connection to algebraic geometry, and their relation to p-adic zeta values in hypersurface families.
Detecting Gauss-Manin and Calabi-Yau Differential Equations
Explore conjectures and criteria for identifying differential equations from Gauss-Manin connections and hypergeometric Calabi-Yau varieties, with a focus on Heun and Painlevé VI equations.