The Nonlinear Stability of Black Holes: An Overview
Explore the mathematical properties of black holes, focusing on their stability as solutions to Einstein's equation and recent proof of nonlinear stability for slowly rotating Kerr black holes.
Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg
Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.
Supersymmetry and Trace Formulas: From Atiyah-Singer to Jacobi-Poisson and Selberg - Part 1
Explore supersymmetry's mathematical origins and applications, from Atiyah-Singer formula to Jacobi-Poisson and Selberg trace formulas, in this advanced mathematics colloquium.
Combinatorial Approximations to the Continuum for Fluid Computation
Explore combinatorial approximations in fluid computation, featuring insights from Dennis Sullivan and Ruth Lawrence-Naimark in this geometry and analysis workshop.
Voigt Boussinesq Equations - Global Regularity and Fluid Dynamics
Explore Voigt Boussinesq equations, their relation to fluid mechanics, and global regularity results for critical cases. Gain insights into incompressible fluid equations and their approximations.
In Search of Euler Equilibria via the Magnetic Relaxation Equations
Explore geometric fluid dynamics, focusing on Euler equilibria and Moffatt's Magnetic Relaxation equations. Delve into recent findings on these mathematically challenging active vector equations with cubic nonlinearity.
Turbulence and Singularities in Fluid Flows - Mathematical Considerations
Explore turbulence, singularities, and fluid dynamics through mathematical considerations, multiscale solutions, and incompressible fluid pressure. Gain insights into Navier-Stokes equations and regularity criteria.
From the Monge Transportation Problem to Einstein's Gravitation Through Euler's Hydrodynamics
Explore the mathematical journey from Monge's transportation problem to Einstein's gravitation, connecting through Euler's hydrodynamics in this insightful lecture.
Non-uniqueness in the Partial Differential Equations of Fluid Dynamics
Explore instability and non-uniqueness in fluid dynamics equations, focusing on recent advancements in Euler and Navier-Stokes equations and their implications for unpredictability.
Can a Scalar Conservation Law Imitate a Diffeomorphism? - Lecture on Fluid Flow Geometry
Explore the representation of scalar convex conservation laws as paths in diffeomorphism spaces, examining weak solutions and their implications for fluid dynamics.
Geometry of Shock Formation and Maximal Development for Euler
Explore the geometry of shock formation and maximal development in Euler equations, focusing on fluid flow analysis and honoring David Ebin's contributions.
Singular Vortex Configurations and Coadjoint Orbits
Explore singular vortex configurations in 2D fluid dynamics, focusing on coadjoint orbits of area-preserving diffeomorphisms and their relation to vortex loops and dipoles.
Emergent Singular Solutions of Nonlinear Wave Equations
Explore nonlinear wave equations and their emergent singular solutions with Imperial College London's Darryl Holm in this advanced mathematics workshop.
Stability of Twisting of Hamiltonian Flows and Applications
Explore Hamiltonian flow stability, twisting phenomena, and their applications in fluid dynamics with insights from Duke University researcher Tarek Elgindi.
ABACUS Tool Suite and MOS Capacitors - Fall 2023
Explore MOS capacitors using ABACUS tool suite. Experiment with doping, structural parameters, and advanced effects in this hands-on semiconductor education session.
ABACUS Tool Suite and PN Junctions - Fall 2023
Explore PN junctions using ABACUS tool suite. Learn about band edge diagrams, charge distributions, and doping effects through interactive simulations powered by industrial-grade technology.
Exploring the Nano World: Building Nanoscale Structures with Polymer Modeler
Explore nanoscale polymer structures using atomic-level simulations. Learn about crystal structures, polymer science paradigms, and use an interactive Polymer Modeler to understand polyacrylonitrile processing and crystallization.
ABACUS Tool Suite: Bandstructure and Band Models - Fall 2023
Explore bandstructure tools in ABACUS, including Kronig-Penney model and sophisticated Tight Binding models. Gain insights into band formation, effective masses, and strain effects in bulk materials and nanowires.
ABACUS Tool Suite Overview and Crystal Structures - Fall 2023
Explore semiconductor crystal structures using the ABACUS tool suite, focusing on visualization, symmetry, and surface properties of silicon crystals.
The Power of Infrared Spectroelectrochemical Techniques in Observing Surface Chemistry
Explore infrared spectroelectrochemical techniques for observing surface chemistry in electrochemistry applications, focusing on nanomaterial electrocatalysts and their role in energy conversion.
Chemistry and Materials with the Amsterdam Modeling Suite
Explore atomistic simulations using Amsterdam Modeling Suite. Learn about AMS driver, DFT engines, force fields, and PARAMS for novel molecular interactions. Gain insights through demos and practical applications.