Dr. Simon Becker


Spring Semester 2024 (current)

Euclidean Harmonic Analysis - Lecture

Mo 12-13

Head TA: Antoine Gagnebin

Lecture notes available here: Download Notes Tex-file

Possible projects:

1.) Hardy-Littlewood Sobolev inequality

2.) Rademacher functions and Khinchine's inequality

3.) The space BMO and the John-Nirenberg inequality

4.) Van der Corput's Lemma

5.) Oscillatory Integral Operators

6.) The fast Fourier transform

7.) Wiener's Tauberian theorem

8.) The Cotlar-Stein lemma

Introduction to Nonlinear Analysis - Seminar

Mo 16-18

Head TA: Antoine Gagnebin

Reference are:

1) Lectures notes by P. Raphael (R)


2) Book by T. Tao (T) (Ch. 5 is not available in the online version)



1) The Schrodinger semigroup (Ch. 5.1 in R) (04.03.) Download Notes

2) Strichartz space-time bounds (Ch. 5.2 in R) (11.03.) Download Notes

3) Local in space decay in weighted spaces (Ch. 5.3 in R) (18.03.)

4) The local Cauchy problem for NLS (Ch. 6.1 in R) (25.03.)

5) Conservation laws and global existence (Ch. 6.2 in R) (08.04.)

6) Scattering and blow up (Ch. 6.3 in R) (22.04.)

7) Variational methods (Ch. 7.1 in R) (29.04.)

8) Study of the minimizers (Ch. 7.2 in R) (13.05.)

Fall Semester 2023

PDE methods in condensed matter physics - Fr 14:15-16:00

Lectures notes by Z. Tao and M. Zworski


Syllabus: Lecture 1: Unbounded operators, Self-adjointness, Kato-Rellich theorem

Lecture 2: Spectral theory, Stability of essential spectra, Agmon distances, Potential well

Lecture 3: Infinitely many wells

Lecture 4: Magnetic Dirac operator

Lecture 5: Bloch-Floquet theory

Lecture 6: Spectrum of magnetic Dirac operator on torus

Lecture 7: Density of states

Lecture 8: Quantum dynamics and RAGE theorem

Lecture 9: Wannier functions

Lecture 10: Vector bundles

Lecture 11: Chern numbers

Lecture 12: Adiabatic/Semiclassical limits

Projects :

1) Bloch-Floquet theory
References: P. Kuchment: https://arxiv.org/pdf/1510.00971.pdf M. Reed B. Simon: Methods of Modern Mathematical Physics. Volume IV: Analysis of Operators

2) Localization of quantum states: References: S. Steinerberger: https://arxiv.org/pdf/1510.06353.pdf

3) Eigenvalues near a potential well: References: B. Simon http://www.numdam.org/article/AIHPA_1983__38_3_295_0.pdf

4) Fredholm theory; References: Chapter 19 (beginning) L. H\"ormander - Pseudo-differential operators https://link.springer.com/book/10.1007/978-3-540-49938-1

5) The integer quantum Hall effect: References: G.M. Graf https://people.phys.ethz.ch/~jshapiro/PDFs/simon_corr.pdf

Operator Algebras and Quantum Info Theory - Fr 10:15-12:00

Book number 1


Book number 2


List of talks: