Lorentzian Geometry Courses and Certifications

Fields Institute

Lorentzian Length Spaces - A Synthetic Approach to Lorentzian Geometry

Explore synthetic approaches to Lorentzian geometry through length spaces, offering new perspectives on spacetime structures and their applications in physics and mathematics.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Sobolev Calculus in Synthetic Lorentzian Geometry

Explore Sobolev calculus in synthetic Lorentzian geometry, focusing on time functions, weak lower differentials, and d'Alembert comparison results in measured Lorentzian length spaces.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Centrum Fizyki Teoretycznej PAN

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.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Centrum Fizyki Teoretycznej PAN

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.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

ICTP Mathematics

Lorentzian Geometry - T. Drumm

Explore Lorentzian geometry, covering basic definitions, hyperbolic spaces, isometries, and advanced concepts like Margulis space-times and crooked planes.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lorentzian Length Spaces: An Introduction to Synthetic Lorentzian Geometry

Explore synthetic Lorentzian geometry foundations, focusing on time separation functions, curvature bounds, and applications in General Relativity, including recent developments in singularity theorems.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Lorentzian Polynomials and the Incidence Geometry of Tropical Linear Spaces

Delve into advanced mathematical concepts exploring Lorentzian polynomials, stable polynomials, and tropical linear spaces through geometric and analytical perspectives.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Between Geometry and Relativity - Summer School

Explore advanced mathematical physics connecting differential geometry with Einstein's general relativity through expert lectures on initial data construction, energy theorems, and spacetime dynamics.

• YouTube
• 14 hours 42 minutes
• On-Demand
• Free Video

ICTP Mathematics

Advanced School and Workshop on Geometry of Discrete Actions

Explore discrete group actions in geometry through hyperbolic spaces, complex dynamics, Teichmüller theory, and holomorphic dynamics with leading mathematicians.

• YouTube
• 1 day 16 hours 38 minutes
• On-Demand
• Free Video

Insights into Mathematics

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.

• YouTube
• 27 minutes
• On-Demand
• Free Video

International Mathematical Union

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.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Properties of the Null Distance on a Spacetime

Explore the null distance concept in spacetime, its definition, examples, and relationship to metric space structures.

• YouTube
• 33 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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.

• YouTube
• 46 minutes
• On-Demand
• Free Video