A Case for Correctly Rounded Math Libraries
Explore the RLIBM project's approach to building correctly rounded elementary functions, revolutionizing polynomial approximations for enhanced mathematical precision in computing.
Numerical Approaches to Modelling Curved Surfaces
Explore numerical methods for modeling curved surfaces, focusing on applications in physics and biology.
Finite Point Blowup for the Critical Generalized Korteweg-de Vries Equation
Explore finite point blowup in critical generalized KdV equations, uncovering new blow-up dynamics and rates. Gain insights into recent advancements in nonlinear wave theory.
Nonlinear Hyperbolic Conservation Laws on Manifolds
Explore nonlinear scalar hyperbolic equations on Riemannian varieties, covering existence, uniqueness, entropy conditions, finite-volume schemes, and numerical results.
Finite Difference Schemes for Partial Differential Equations in Oceanography - Munk Equation and Shallow Water Equations
Explore high-order finite difference schemes for Munk equation and Shallow Water equations on Cubed Sphere grid, with numerical and convergence analysis.
Multilevel Monte Carlo Methods for the Dean-Kawasaki Equation from Fluctuating Hydrodynamics
Explore Multilevel Monte Carlo methods for Dean–Kawasaki equation, analyzing efficiency and convergence in stochastic PDEs of Fluctuating Hydrodynamics for many-particle systems.
Designing Conservative and Accurately Dissipative Numerical Integrators in Time
Explore innovative framework for structure-preserving time steppers using finite elements and auxiliary variables. Discover applications in Kepler, Kovalevskaya, Navier-Stokes, and Benjamin-Bona-Mahony problems.
New Algorithms: Numerical Solution of Large Systems of Nonlinear Equations Using Monodromy
Explore a novel algorithm using monodromy to solve large systems of analytic nonlinear equations, developed during a Wolfram internship.
Computational Mathematics: Dynamics, Geometry, and Algebra in Numerical Integration
Explore computational mathematics at the intersection of dynamics, geometry, and algebra, focusing on geometric numerical integration and structure-preserving discretization of differential equations.
Modeling X with Partial Differential Equations
Explore advanced PDE modeling techniques using NDSolve and finite element methods for engineering applications, including axisymmetric regions and hyperelastic solid mechanics.
PDEs for Neural Assemblies - Analysis, Simulations, and Behavior
Explore PDEs for neural assemblies, analyzing their behavior through simulations and mathematical techniques with Professor Benoît Perthame from Sorbonne University.
Optimization in Theory and Practice
Explore optimization techniques and their real-world applications with insights from Stephen Wright of University of Wisconsin-Madison, blending theoretical foundations and practical implementations.
Approximately Hadamard Matrices and Random Frames
Explore approximately Hadamard matrices and random frames with Mark Rudelson, delving into advanced mathematical concepts and their applications in signal processing and data analysis.
Numerical Methods for SDEs with Singular Coefficients - Lecture 3
Explore numerical methods for SDEs with singular coefficients in this advanced mathematics lecture by Benjamin Jourdain, focusing on cutting-edge techniques and applications.
Numerical Methods for SDEs with Singular Coefficients - Lecture 1
Explore numerical methods for stochastic differential equations with singular coefficients in this advanced mathematics lecture by Benjamin Jourdain.
Numerical Methods for SDEs with Singular Coefficients - Lecture 2
Explore numerical methods for SDEs with singular coefficients in this advanced mathematics lecture by Benjamin Jourdain, focusing on cutting-edge techniques and applications.
Numerical Quadrature for Singular Integrals over Self-Similar Measures on Fractal Sets
Explore numerical quadrature techniques for singular integrals over self-similar measures on fractal sets, focusing on advanced mathematical concepts and applications.
Monte Carlo Guided Diffusion for Bayesian Linear Inverse Problems
Explore Monte Carlo guided diffusion techniques for solving Bayesian linear inverse problems in this advanced mathematical presentation by Sylvain Le Corff.
Optimality of Algorithms for Approximation and Computation - Rothschild Lecture
Explore optimality in approximation and computation algorithms with Prof. Ronald DeVore's in-depth analysis of mathematical techniques and their applications in data science.
Image Compression with Differential Equations
Explore innovative image compression techniques using partial differential equations, combining mathematical modeling, optimization, and numerical methods for efficient data encoding and reconstruction.
Solving PDEs in Domains with Complex Evolving Morphology - Rothschild Lecture
Explore mathematical challenges in solving PDEs on evolving domains, focusing on biological applications. Learn abstract frameworks, well-posedness theory, and numerical methods for complex geometries.