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

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

First Order Differential Equations in Characteristic Zero and Characteristic p

Explore advanced mathematical concepts of first-order differential equations across characteristic zero and characteristic p, with insights from leading mathematician Marius van der Put.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Higher Dimensional Katz Theory

Explore advanced mathematical concepts in higher dimensional Katz theory through rigorous analysis and theoretical frameworks within singular differential equations.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Picard-Fuchs Equations and Modular Forms - Applications and Theory

Explore the intricate relationship between Picard-Fuchs equations and modular forms, examining their mathematical applications and theoretical foundations in algebraic differential equations.

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

G-Functions of Differential Order 2

Delve into advanced mathematical concepts exploring G-functions of differential order 2, focusing on algebraicity and transcendence properties in singular differential equations.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Differential Galois Theory and the Algebraicity of Solutions - Part 3

Delve into advanced concepts of Differential Galois Theory, exploring algebraicity of solutions and their applications in singular differential equations with mathematician Michael Singer.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Differential Equations, Geometry and Arithmetic - Lecture 3

Delve into advanced mathematical concepts exploring the intricate relationships between differential equations, geometry, and arithmetic through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 29 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

Gravitational-Wave Wave Optics Lensing Simulations and Phenomenology

Explore the fascinating physics of gravitational-wave lensing, from detection methods to wave optics phenomena, and understand how massive objects influence these cosmic ripples in spacetime.

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

Spin Wave Optics of Gravitational Waves - Wave Effects Beyond Geometric Optics

Delve into gravitational wave lensing physics, exploring wave and spin effects beyond geometric optics to understand black holes and matter distribution in the universe.

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

Gravitational Lensing in the Presence of Plasma - Theory and Observations

Explore gravitational lensing phenomena around black holes and compact objects, focusing on plasma effects, photon spheres, shadow formations, and their implications for radio observations.

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

Why Are LIGO/Virgo Black Holes So Massive? - Understanding Mass Measurement in Gravitational Wave Astronomy

Explore how gravitational lensing and Doppler effects from nearby supermassive black holes may influence our measurements of LIGO/Virgo black hole masses and our understanding of cosmic evolution.

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

Measuring Proper Motion of Gravitational Wave Sources with Strong Lensing Events

Explore how strong gravitational lensing enables measurement of gravitational wave source velocities through multiple image analysis and its implications for future telescopes and cosmology.

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

High-Frequency Approximation in Gravitational Lensing and Wave Optics

Explore the intersection of geometric optics and gravitational lensing, examining Green functions and field properties to understand high-frequency approximations in strong gravity scenarios.

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