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#Lorentzian Geometry

Showing: 26 courses
ICTP Mathematics

Lorentzian Geometry - T. Drumm

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Explore Lorentzian geometry, covering basic definitions, hyperbolic spaces, isometries, and advanced concepts like Margulis space-times and crooked planes.
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13 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Insights into Mathematics

Colored Spreads and Generalizations in Rational Trigonometry - Lecture 2

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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.
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8 Lesons
27 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

On the Regularity Implied by the Assumptions of Geometry

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Explore the theory of Regularity Transformation equations and their impact on non-regular spacetime geometry, including applications in General Relativity and Einstein-Euler equations.
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1 Lesons
46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Lorentzian Analog for Hausdorff Dimension and Measure

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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.
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1 Lesons
36 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lorentzian Functors and Closures of Relevant Subsets of Lorentzian Gromov-Hausdorff Space

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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.
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1 Lesons
44 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality

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Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.
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1 Lesons
38 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds

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Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.
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1 Lesons
49 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Lecture 4

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part II

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part I

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
47 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Spectral Theory of Stationary Spacetimes - Part I

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Explore spectral theory in stationary spacetimes, delving into mathematical concepts at the intersection of relativity and quantum mechanics.
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1 Lesons
59 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Globally Hyperbolic Anti-de Sitter Manifolds and Compact Clifford-Klein Forms

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Explore globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms in advanced geometry, focusing on curvature and rigidity concepts.
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1 Lesons
50 minutes
On-Demand
Free-Video
NCCR SwissMAP

The Lorentzian Scattering Rigidity Problem and Rigidity of Stationary Metrics

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Explore analytic techniques in dynamics and geometry, focusing on Lorentzian scattering rigidity and stationary metrics.
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14 Lesons
54 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Spacetime G-structures - Lecture 3

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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.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Spacetime G-structures I - Introduction to Klein Models and Associated Geometries

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Explore spacetime G-structures, focusing on Klein models, associated G-structures, and intrinsic torsion classification for Carrollian, Galilean, and Lorentzian geometries in theoretical physics.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
International Mathematical Union

Jonathan Luk- Singularities in General Relativity

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Explore singularities in general relativity, from fundamental concepts to advanced topics like Schwarzschild and Kerr spacetimes, cosmic censorship, and gravitational collapse.
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24 Lesons
47 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Nonsmooth Approach to Einstein's Theory of Gravity

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Explore a nonsmooth approach to Einstein's gravity theory, focusing on reformulating curvature concepts and developing a synthetic null energy condition for Lorentzian spaces.
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1 Lesons
41 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Timelike Ricci Bounds and Einstein's Theory of Gravity in Non-Smooth Settings

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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.
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1 Lesons
46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces

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Explore global timelike curvature bounds in Lorentzian length spaces, examining Alexandrov's Patchwork analogue and Bonnet-Myers theorem applications for spacetime geometry.
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1 Lesons
31 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Gromov's Reconstruction Theorem and Measured Gromov-Hausdorff Convergence in Lorentzian Spaces

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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.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Properties of the Null Distance on a Spacetime

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Explore the null distance concept in spacetime, its definition, examples, and relationship to metric space structures.
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1 Lesons
33 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Global Hyperbolicity Through the Eyes of the Null Distance

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Explore global hyperbolicity in spacetime geometry through null distance, encoding causal information in metric space structures and characterizing completeness.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Constructing Distance Realizers via Midpoints in Lorentzian Mid-Length Space

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Explore Lorentzian pre-length spaces, null distance, and midpoint properties to construct distance realizers between timelike related points in non-regular spacetime geometry.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lorentzian Length Spaces: An Introduction to Synthetic Lorentzian Geometry

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Explore synthetic Lorentzian geometry foundations, focusing on time separation functions, curvature bounds, and applications in General Relativity, including recent developments in singularity theorems.
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1 Lesons
51 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

On the Classification Problem for Static Metrics with Positive Cosmological Constant

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Explore recent advances in classifying static solutions to vacuum Einstein field equations with positive cosmological constant and related mass concepts in general relativity.
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1 Lesons
59 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Non-Regular Spacetime Geometry via Metric Measure Geometry

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Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.
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1 Lesons
34 minutes
On-Demand
Free-Video