Our Changing Climate System
Explore the ongoing climate change, its impacts, and the urgent need for global action with insights from glaciologist Georg Kaser on irreversible changes and the Paris Agreement.
A Nonsmooth Approach to Einstein's Theory of Gravity
Explore a nonsmooth approach to Einstein's gravity theory, focusing on reformulating curvature concepts and developing a synthetic null energy condition for Lorentzian spaces.
Timelike Ricci Bounds and Einstein's Theory of Gravity in Non-Smooth Settings
Explore Lorentzian synthetic spaces, optimal transport theory, and timelike Ricci curvature bounds to characterize Einstein's equations in non-smooth spaces, with applications to gravity.
Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces
Explore global timelike curvature bounds in Lorentzian length spaces, examining Alexandrov's Patchwork analogue and Bonnet-Myers theorem applications for spacetime geometry.
Gromov's Reconstruction Theorem and Measured Gromov-Hausdorff Convergence in Lorentzian Spaces
Explore Lorentzian space convergence, Gromov reconstruction theorem, and measured Lorentz-Gromov-Hausdorff convergence in nonsmooth general relativity. Gain insights into isomorphy of measured Lorentzian spaces.
Generalizations of Classical Relativity Theorems
Explore generalizations of classical relativity theorems, focusing on averaged energy conditions and their implications for singularity and area theorems in semiclassical gravity.
Null Shells: Abstract Formulation of Junction Conditions and Particularization
Explore abstract formulation of junction conditions for matching spacetimes, focusing on null shells and their gravitational/matter content. Analyze multiple matchings and cut-and-paste scenarios.
Spacetime Geometry of Spin, Polarization, and Wavefunction Collapse
Explore a new spacetime geometry incorporating quantum nonlocality into general relativity, examining implications for spin-1/2 fermions and the Born rule.
The Space of Causal Diamonds as a Lorentzian Pre-Length Space
Explore causal diamonds in Mathematical Relativity, examining their geometry and geodesic structure when endowed with Hausdorff distance, and their implications for metric convergence stability.
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.
Properties of the Null Distance on a Spacetime
Explore the null distance concept in spacetime, its definition, examples, and relationship to metric space structures.
Global Hyperbolicity Through the Eyes of the Null Distance
Explore global hyperbolicity in spacetime geometry through null distance, encoding causal information in metric space structures and characterizing completeness.
Constructing Distance Realizers via Midpoints in Lorentzian Mid-Length Space
Explore Lorentzian pre-length spaces, null distance, and midpoint properties to construct distance realizers between timelike related points in non-regular spacetime geometry.
Waves and Wind-Driven Flows in the Ocean - Lecture 2
Explore Kelvin-Stuart vortices in fluid mechanics, plasma physics, and planetary rings. Analyze stability, applications, and magnetic island equilibria in 2D ideal MHD equations.
Ocean Modeling: Stochastic Approaches to Numerical Simulations
Explore stochastic approaches in ocean modeling, including Monte-Carlo methods, perturbed initial conditions, and stochastic boundary conditions and dissipation operators for improved numerical simulations.
Waves and Wind-Driven Flows in the Ocean - Lecture 4
Explore Kelvin-Stuart vortices' stability in fluid mechanics, plasma physics, and planetary rings. Analyze nonlinear stability and linear instability for various perturbations.
Massive Waves Gravitationally Bound to Static Bodies
Explore massive waves bound to static bodies in astrophysical spacetimes. Discover standing wave solutions and their implications for Klein-Gordon equations on asymptotically conic manifolds.
Nonlinear Stability of Kerr-de Sitter Spacetimes
Explore nonlinear stability of slowly-rotating Kerr-de Sitter black holes, focusing on a new proof using vectorfield method and bootstrap scheme to uncover high-frequency spectral gap.
Wave Equations in Kerr-de Sitter Spacetimes - The Full Subextremal Range
Explore wave equations in Kerr-de Sitter spacetimes, extending Vasy's results to the full subextremal range and analyzing photon trapping around black holes.
Feynman Propagators on Curved Spacetime
Explore Feynman propagators on curved spacetime, their construction, and connection to quantum states. Delve into microlocal techniques and their application to wave and Dirac-type operators.
Infrared Finite Scattering Theory in QFT and Quantum Gravity
Explore infrared finite scattering theory in QFT and quantum gravity, addressing IR divergences, memory effects, and challenges in constructing IR-finite S-matrices across various theories.