Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

Null and Timelike Circular Orbits: Insights from Effective 2D Metrics

Explore how spacetime symmetries enable mapping 4D geodesics to lower dimensions, examining circular orbits around black holes and their stability in strong gravitational fields.

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

Multi-messenger Gravitational Lensing and the Vera C. Rubin Observatory

Explore multi-messenger gravitational lensing discoveries through the Vera Rubin Observatory's capabilities, focusing on binary compact object mergers and electromagnetic observations.

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

The Black Hole Photon Ring: Understanding M87* and Future NASA Observations

Explore the fascinating physics of black hole photon rings, their role in testing general relativity, and their potential detection through NASA's future Black Hole Explorer mission.

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

Black Holes as Laboratories - Searching for Ultralight Fields

Explore how black holes can detect ultralight boson fields through superradiant extraction, and discover their potential role in fundamental physics research using the Event Horizon Telescope.

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

Bi-local Approach to Geometrical Optics in General Relativity

Explore advanced geometrical optics in General Relativity through bi-local geodesic operators, examining spacetime optical properties and the relationship between parallax and angular diameter distances.

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

Exact Wave-Optical Imaging of Black Hole Spacetimes

Delve into wave-optical imaging techniques for black holes, exploring analytical methods using Green's functions and Teukolsky equations to understand shadow formation in Kerr-de Sitter spacetime.

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

Gravitational Wave Lensing: Current Searches and Future Prospects

Explore gravitational wave lensing's role in understanding dark matter, distant black holes, and gravity's wave-optics regime through current research findings and future detection possibilities.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

P-adic Differential Equations Over Berkovich Curves

Dive into advanced mathematical concepts exploring p-adic differential equations and their behavior over Berkovich curves, with insights from leading researcher Andrea Pulita.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

On Katz' Nilpotence Conjecture, p-Determinants, and q-Generalization

Delve into advanced mathematical concepts exploring Katz' nilpotence conjecture, examining p-determinants and their q-generalizations through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 41 minutes
• On-Demand
• Free Video

On Abel's Problem and Gauss Congruences

Delve into advanced mathematical concepts exploring Abel's problem and Gauss congruences, examining their relationships and implications in differential equations and number theory.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

The Arithmetic of Power Series and Applications to Periods

Explore the mathematical foundations of power series arithmetic and their relationship to periods, focusing on singular differential equations and their applications.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Towards a Kontsevich-Zagier Type Conjecture for Holonomic Series

Delve into advanced mathematical concepts exploring holonomic series and their relationship to the Kontsevich-Zagier conjecture through rigorous theoretical analysis.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Ice Clouds Over the Asian Monsoon and Their Role in the Global Climate

Explore the formation and impact of ice clouds in the Asian Summer Monsoon system, examining their crucial role in climate patterns and water vapor transport through aircraft-based observations and simulations.

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

Extending Hölder's Result on the Differential Transcendence of the Gamma Function

Delve into advanced mathematical concepts exploring Hölder's theorem and its extension to the differential transcendence properties of the Gamma function through rigorous analysis.

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

Arithmetic Algebraization Theorems and the Analogy Between Number Fields and Function Fields

Delve into advanced mathematical concepts exploring arithmetic algebraization theorems and their relationship with number fields through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video