Anomalous Dissipation and the Strong Onsager Conjecture - Part 2: L^3 Convex Integration
Explore anomalous dissipation and the Strong Onsager Conjecture in turbulent flows, focusing on L^3 convex integration techniques for mathematical analysis of energy transfer.
Quantum Algorithms for Multiscale Partial Differential Equations
Explore quantum algorithms for multiscale PDEs, focusing on Schrödingerisation method and its quantum circuit implementation. Learn applications to linear multiscale PDEs and Hamilton-Jacobi equations.
Lyapunov Exponents of the Navier-Stokes Equations
Explore Lyapunov exponents in Navier-Stokes equations through Alex Blumenthal's conference talk, delving into probabilistic techniques for random and time-dependent dynamical systems.
Construction of Boltzmann and McKean Vlasov Type Flows - The Sewing Lemma Approach
Explore construction of Boltzmann and McKean Vlasov flows using the sewing lemma approach. Gain insights into stochastic analysis and numerical probability from expert Vlad Bally.
The Landau Hamiltonian with Delta-Potentials Supported on Curves
Explore the Landau Hamiltonian with delta-potentials on curves in this mathematical conference talk. Gain insights into spectral analysis for quantum Hamiltonians.
Suppression of Chemotactic Blow-up by Buoyancy
Explore the suppression of chemotactic blow-up by buoyancy in this mathematical conference talk, featuring insights on aggregation-diffusion equations and collective behavior.
Hardy Inequalities for Magnetic p-Laplacians
Explore Hardy inequalities for magnetic p-Laplacians in this mathematical conference talk, delving into advanced concepts and their applications in physics and analysis.
Wasserstein Gradient Flows and Applications to Sampling in Machine Learning - Lecture 2
Explore Wasserstein gradient flows and their applications to sampling in machine learning, focusing on advanced mathematical concepts and techniques.
The Mean-Field Limit of Non-Exchangeable Integrate and Fire Systems
Explore mean-field limits in non-exchangeable integrate and fire systems with Pierre-Emmanuel Jabin. Delve into advanced mathematical concepts and their applications in this specialized conference talk.
Soliton Resolution and Channels of Energy for Nonlinear Wave Equations
Explore soliton resolution and energy channels in nonlinear wave equations with Carlos Kenig's lecture at IMPA's 70th anniversary conference, featuring cutting-edge mathematical research.
Some Mass Concepts in General Relativity
Explore new PDE-based approaches to fundamental results in mathematical general relativity, including positive mass theorem and Riemannian Penrose inequality.
Mathematical General Relativity: Seventy-Two Years After Yvonne Bruhat's Foundational Acta Paper
Explore key achievements in mathematical general relativity since Y.C Bruhat's foundational Acta paper, reviewing 72 years of progress in the field.
Formation of Quiescent Big Bang Singularities
Explore general relativity's big bang singularities, recent stability results, and a new condition for big bang formation in Einstein-non-linear scalar field settings.
Dispersion Estimates for Dirac Equations with Aharonov-Bohm Magnetic Fields
Explore dispersive properties of 2D Dirac operators with Aharonov-Bohm potentials, examining flow components and deducing sharp Strichartz estimates for advanced mathematical analysis.
Weakly Turbulent Solution to the Schrödinger Equation on the 2D Torus with Potential
Explore a smooth solution to the linear Schrödinger equation on a 2D torus, examining logarithmic H^1 Sobolev norm growth and infinite-time blowup using adapted CKSTT techniques.
The Modified Energy Method for a Nonlocal Quasilinear Wave Equation
Explore nonlinear waves and relativity through the modified energy method for a nonlocal quasilinear wave equation in this advanced mathematics lecture.
Kolmogorov-Arnold Networks - Alternatives to Multi-Layer Perceptrons
Explore Kolmogorov-Arnold Networks as alternatives to MLPs, offering improved accuracy and interpretability in data fitting and PDE solving. Discover their potential for scientific collaboration and law discovery.
Kirk Lecture: A Recent Technology for Scientific Computing - The Virtual Element Method
Explore the Virtual Element Method, a generalization of FEM for solving PDEs using polygonal/polyhedral meshes, offering improved accuracy, efficiency, and flexibility in scientific computing.
Secure Numerical Computations Using Fully Homomorphic Encryption
Explore secure cloud computing with homomorphic encryption using Julia packages. Learn to protect sensitive data while performing numerical computations on untrusted systems.
PirateNets - Physics-Informed Deep Learning with Residual Adaptive Networks
Explore PirateNets: a novel deep learning architecture for solving PDE-governed problems, offering improved stability and efficiency over traditional physics-informed neural networks.
Model-Constrained Deep Learning Approaches for Scientific Machine Learning
Explore model-aware machine learning methods combining scientific computing and data-driven models. Learn about ROM-ML and Autoencoder-based Inversion approaches for PDE-constrained inverse problems.