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

Spectral Theory of Stationary Spacetimes - Lecture 4

Explore advanced concepts in spectral theory applied to stationary spacetimes, delving into mathematical relativity and its implications for understanding spacetime structures.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Classically Forbidden Regions and Analytic Hypoellipticity in Spectral Theory

Explore analytic microlocal methods in condensed matter physics, focusing on magic angles in graphene and eigenfunction decay. Discover insights from numerical simulations and potential research directions.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Microlocal Methods for Operators with Analytic Coefficients - Lecture 3

Explore advanced microlocal methods for operators with analytic coefficients in this in-depth mathematical analysis lecture by Maciej Zworski.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Spectral Theory of Stationary Spacetimes - Lecture 3

Explore advanced concepts in spectral theory of stationary spacetimes, building on previous lectures in the series.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Microlocal Methods for Operators with Analytic Coefficients - Lecture 2

Explore advanced microlocal methods for operators with analytic coefficients in mathematical physics and spectral theory.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Spectral Theory of Stationary Spacetimes - Part II

Explore advanced concepts in spectral theory applied to stationary spacetimes, building on foundational knowledge in mathematical relativity and quantum mechanics.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Spectral Theory of Stationary Spacetimes - Part I

Explore spectral theory in stationary spacetimes, delving into mathematical concepts at the intersection of relativity and quantum mechanics.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Microlocal Methods for Operators with Analytic Coefficients - Lecture 1

Explore microlocal methods for operators with analytic coefficients in this advanced mathematics lecture by Maciej Zworski.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Initial Data Rigidity via Dirac-Witten Operators

Explore initial data rigidity in spin settings using Dirac-Witten operators. Derive a rigidity theorem for manifolds with boundary, examining dominant energy conditions and null expansion scalars.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Massive Waves Gravitationally Bound to Static Bodies

Explore massive waves bound to static bodies in astrophysical spacetimes. Discover standing wave solutions and their implications for Klein-Gordon equations on asymptotically conic manifolds.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Semi-classical Approximation for Time-dependent Systems

Explore semi-classical approximations for time-dependent systems, focusing on initial value representations and their applications in mathematical relativity and theoretical chemistry.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Modeling Planetary-Scale Fluid Flows in the Laboratory

Explore planetary-scale fluid dynamics through laboratory experiments, from Rossby waves to exoplanet atmospheres. Gain insights into climate transitions and extreme weather patterns.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Stratospheric Planetary Flows from the Perspective of the Euler Equation on a Rotating Sphere

Explore stratospheric planetary flows through the lens of the Euler Equation on a rotating sphere, delving into the dynamics of large-scale fluid movements.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Dynamics Near a Shear Flow with Coriolis Force

Explore the impact of Coriolis force on large-scale fluid dynamics, focusing on shear flows under beta-plane approximation and their unique spectral properties.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Waves on the β-Planes in the Presence of a Mean Zonal Flow - Beyond the Doppler Shift

Explore waves on β-planes with mean zonal flow, analyzing eigenvalue equations, dispersion curves, and instabilities in rotating shallow water systems.

• YouTube
• 40 minutes
• Self-Paced
• Free Video