Lorentzian Geometry - T. Drumm
Explore Lorentzian geometry, covering basic definitions, hyperbolic spaces, isometries, and advanced concepts like Margulis space-times and crooked planes.
Colored Spreads and Generalizations in Rational Trigonometry - Lecture 2
Explore colored spreads in planar geometries, visualizing red and green spreads using cross products and determinants. Learn about generalized dot products and Pythagoras' theorem in different geometries.
On the Regularity Implied by the Assumptions of Geometry
Explore the theory of Regularity Transformation equations and their impact on non-regular spacetime geometry, including applications in General Relativity and Einstein-Euler equations.
A Lorentzian Analog for Hausdorff Dimension and Measure
Explore a novel approach to geometric dimension in Lorentzian spaces, comparing it to Hausdorff dimension and examining applications in spacetime analysis and synthetic curvature bounds.
Lorentzian Functors and Closures of Relevant Subsets of Lorentzian Gromov-Hausdorff Space
Explore recent advances in Lorentzian length spaces theory, including stability of properties, denseness of causal spacetimes, and geometric conditions for Radon measures in Lorentzian Gromov-Hausdorff space.
Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality
Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.
A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds
Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.
Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Lecture 4
Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part II
Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part I
Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
Spectral Theory of Stationary Spacetimes - Part I
Explore spectral theory in stationary spacetimes, delving into mathematical concepts at the intersection of relativity and quantum mechanics.
Globally Hyperbolic Anti-de Sitter Manifolds and Compact Clifford-Klein Forms
Explore globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms in advanced geometry, focusing on curvature and rigidity concepts.
The Lorentzian Scattering Rigidity Problem and Rigidity of Stationary Metrics
Explore analytic techniques in dynamics and geometry, focusing on Lorentzian scattering rigidity and stationary metrics.
Spacetime G-structures - Lecture 3
Explore spacetime G-structures, focusing on Klein models, associated G-structures, and intrinsic torsion. Gain insights into carrollian, galilean, and lorentzian geometries and their applications in physics.
Spacetime G-structures I - Introduction to Klein Models and Associated Geometries
Explore spacetime G-structures, focusing on Klein models, associated G-structures, and intrinsic torsion classification for Carrollian, Galilean, and Lorentzian geometries in theoretical physics.
Jonathan Luk- Singularities in General Relativity
Explore singularities in general relativity, from fundamental concepts to advanced topics like Schwarzschild and Kerr spacetimes, cosmic censorship, and gravitational collapse.
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.
Properties of the Null Distance on a Spacetime
Explore the null distance concept in spacetime, its definition, examples, and relationship to metric space structures.