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.
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.
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.
Uniqueness and Non-Uniqueness for Percolation on Groups
Explore percolation theory on groups, examining uniqueness and non-uniqueness of infinite clusters and their connections to group-theoretic concepts.
Elements of General Relativity - Lecture 2
Explore advanced concepts in general relativity, focusing on geometry beyond Riemann and examining curvature and rigidity in spacetime.
Elements of General Relativity - Lecture 3
Explore advanced concepts in general relativity, focusing on geometry beyond Riemann and examining curvature and rigidity in spacetime.
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.
On the Classification Problem for Static Metrics with Positive Cosmological Constant
Explore recent advances in classifying static solutions to vacuum Einstein field equations with positive cosmological constant and related mass concepts in general relativity.
A Quiescent Regime for Big Bang Formation
Explore stable big bang formation in general relativity, covering recent results and a new condition for big bang formation in Einstein-non-linear scalar field settings.
Mathematical General Relativity: Seventy-Two Years After Yvonne Bruhat's Foundational Acta Paper
Explore key achievements in mathematical general relativity since Y.C Bruhat's foundational Acta paper, reviewing 72 years of progress in the field.
Mass Aspect Function for Weakly Regular Asymptotically Hyperbolic Manifolds
Explore mass aspect function definition for weakly regular asymptotically hyperbolic manifolds, extending Wang's work to low regularity settings using cut-off functions and distribution theory.
Formation of Quiescent Big Bang Singularities
Explore general relativity's big bang singularities, recent stability results, and a new condition for big bang formation in Einstein-non-linear scalar field settings.
Non-Regular Spacetime Geometry via Metric Measure Geometry
Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.
Anisotropic Scale-Separated AdS Flux Vacua
Explore anisotropic scale-separated AdS flux vacua in string theory, examining their properties and implications for the landscape/swampland program.
Set Valued Hamilton-Jacobi-Bellman Equations - Applications and Theory
Explore set valued PDEs and their applications in stochastic optimization, risk measures, and game theory. Learn about dynamic programming principles and set valued HJB equations.
Machine Learning Calabi-Yau Metrics - Landscapia
Explore machine learning techniques for Calabi-Yau metrics in string theory, focusing on applications in the Landscapia project and their implications for theoretical physics.
Equivariant Localization in Supergravity
Explore equivariant localization in supergravity with James Sparks, delving into advanced concepts in theoretical physics and holography.
Geometry, Topology and Discrete Symmetries Revealed by Deep Neural Networks
Explore deep neural networks' ability to reveal geometry, topology, and discrete symmetries in manifolds. Learn about universal approximators and their applications in inverse problems and group actions.
Flows on Graded Manifolds - Part II
Explore advanced concepts of flows on graded manifolds, delving into complex mathematical physics topics with expert Jan Vysoký.