The summer school addresses doctoral students and postdoctoral researchers, and also welcomes more experienced scientists.
In addition to the three lecture series, there is time for a limited number of talks by participants.
David Borthwick
(Emory University)
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Resonances in Geometric Scattering Theory
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Tanya Christiansen
(University of Missouri)
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Resonances and Schrödinger Operators
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David Hasler
(Friedrich Schiller University Jena)
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Random Schrödinger Operators
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Recommended background knowledge: (
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- Measure Theory and Integration
- Basics of Banach and Hilbert Spaces
- Basics of Functional Analysis
- Bounded linear operators
- Self-adjoint operators
- Compact operators
- Spectrum of a bounded operator
- Spectral theorem for bounded operators
- Stone's theorem
- Schrödinger operator basics
- Schrödinger operator as a self-adjoint operator
- Scattering theory for Schrödinger operator (resolvent, scattering matrix)
- Definition of a scattering resonance
- Laplacian on a Riemannian manifold
- Definition
- Self-adjointness
- Spectrum on compact versus non-compact manifolds
- Complex analysis
- Analytic functions
- Meromorphic functions
- Laurent series
- Differential geometry
- Definition of Riemannian metric, Riemannian manifolds, (geodesic) completeness
- Definition of constant curvature spaces (esp. Poincaré plane and upper Poincaré half-space)
- Discrete group actions
- Limit sets
- Convex co-compact hyperbolic manifolds
