Department Mathematik
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Marcel Schaub

Mathematisches Institut der Universität München
Theresienstr. 39
D-80333 München

Email: schaub [at] math.lmu.de

Phone:   +49 (0)89   2180 4407
Room: B407
Office Hours: Only via eMail until further notice.

Arbeitsgruppe Analysis, Mathematische Physik und Numerik


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Teaching

Analysis einer Variablen with Prof. Dr. Peter Müller

Previous Teaching in Müchen

Previous Teaching in Tübingen

  • Winter 2017/18: Mathematical Quantum Theory (site does not exist anymore; Version of WS2018/19). Here are the former problems and the corresponding notes.
  • Summer 2018: Analysis II (links on site may be scrambled due to a major reconstruction of the Tübingen website).
  • Winter 2018/19: Seminar Analysis

Research Interests

  • BCS-Theory of superconductivity and the constant magnetic field like in FHSS12 or FHL17
  • Adiabatic Theory for Extended Quantum Systems like in BRF17 and exponential estimates à la HJ01 for the adiabatic theorem therein.

Lecture Notes

Here are some TeX'ed lecture notes from the lectures I attended in Munich that you might find useful for your studies. If you find mistakes/typos, please let me know (via the e-mail above). Note that the e-mail-address frequently written in the notes is not valid anymore. There is no guarantee on correctness.

  • Analysis II (german): Metric spaces and differential calculus in euclidean space.
  • Analysis III (german): Measures and integration theory, differential forms on manifolds.
  • Functional Analysis 1 (english): topological spaces, Banach-/Hilbert spaces, bounded linear operators, weak-/weak*-topologies and -convergence, cornerstones (Baire, Hahn-Banach, uniform boundedness principle, open mapping), compact operators.
  • Functional Analysis 2 (english): spectral theory and functional calculus for compact, bounded self-adjoint, and unbounded self-adjoint operators; projection valued measures, existence of self-adjoint extensions
  • PDE 1 (german): solution theory to transport, Laplace/Poisson, heat, and wave equation; weak derivatives and Sobolev spaces (only 1-d).
  • PDE 2 (english): uniformly elliptic, linear equations of 2nd order. Weak derivatives, Sobolev spaces on bounded domains, approximation of Sobolev functions, extension, trace, embeddings; weak solutions (existence, uniqueness, continuity in "data"), elliptic regularity.
  • Semilinear elliptic PDE 1 and 2 (english): Differential calculus in Banach-/Hilbert spaces, existence of weak solutions to semilinear elliptic equations via direct method and minimax methods; convexity, coercivity, (sub)critical growth, abstract result on admissible minimax-classes, mountain pass theorem, saddle point theorem; constrained minimization, fixpoint methods.
  • Distributions and Sobolev spaces (german): topology on smooth functions with compact support, distributions, convolution, Fourier transform, fundamental solutions, Sobolev embeddings (continuous and compact), trace operator, fractional Sobolev spaces.
  • Mathematical Quantum Mechanics 1 (english): stability of matter (first & second kind), electrostatics, instability of second kind for bosons.
  • Mathematical Quantum Mechanics 2 (english): scattering theory; RAGE theorem, wave operators, asymptotic completeness via Cook's, trace-class-, and Enß-method; Von-Neumann-Schatten-classes, relative boundedness and compactness. Here is a different type of Mathematical Quantum Mechanics course by Prof. Jan Philip Solovej from Copenhagen and some work I did on the problems therein.