# Teaching

## Quantum Mechanics for Mathematicians (Spring 2020)

### Materials:

- List of homework exercises
- Lecture notes:
- Lie algebras and the Poisson bracket
- Lie groups
- Group actions and Noether’s theorem
- Integrable systems and Arnold-Liouville theorem
- Classical mechanics
- Hamiltonian and Liouville dynamics
- Operators on Hilbert spaces
- Axioms of Quantum Mechanics
- Spectral Theorem
- Heisenberg’s uncertainty relations
- Quantization and quantum dynamics
- Schrödinger’s equations

- Literature:

## Symplectic Geometry and Hamiltonian Dynamics (Spring 2019)

### Materials:

- Syllabus and course plan
- List of Homework Exercises
- Notes:
- Literature:
- A. Cannas Da Silva. Lectures on symplectic geometry, volume 1764. Springer Science & Business Media, 2001.
- H. Geiges. An introduction to contact topology, volume 109. Cambridge University Press, 2008.
- H. Hofer and E. Zehnder. Symplectic invariants and Hamiltonian dynamics. Birkhauser Advanced Texts: Basler Textbooks. Birkhauser Verlag, Basel, 1994.
- D. McDuff and D. Salamon. Introduction to symplectic topology. Oxford Mathematical Monographs. Oxford University Press, 2005.

## Seminar on Vector Bundles in Algebraic Topology (Spring 2018)

- Course description in the catallogue
- Syllabus and Seminar’s schedule
- The book we will be following is Allen Hatcher's Vector Bundles and K-Theory

### Notes:

- Classifying vector bundles by Samuel Koovey
- Clutching functions for $S^{n}$ by Nadir Bayo
- The K Functor by Max Gheorghiu
- The Fundamental Product Theorem Part I by Muriel Egli
- The Fundamental Product Theorem Part II by Samet Armagan
- The Fundamental Product Theorem Part III by Phillipp Provenzano
- Bott Periodicity Theorem by Davide Matasci
- K-cohomology by Mirja Zuber
- Division Algebras and Parallelizable Spheres part I by Mojgan Hosseinzadeh
- Division Algebras and Parallelizable Spheres part II by Jerome Wettstein
- Division Algebras and Parallelizable Spheres part III by Ramon Braunwarth
- Universal Bundle and Grassmannians by David Lanners
- Stiefel-Whitney classes and Chern classes part I by Shengxuan Liu
- Stiefel-Whitney classes and Chern classes part II by Muze Ren
- Stiefel-Whitney classes and Chern classes part III by Antonia Giannopoulou
- Cell structures on Grassmannians by Malcolm Cameron
- Applications of Stiefel-Whitney classes and Chern classes by Oliver Edtmair
- Obstructions to sections part I by Gilles Englebert
- Obstructions to sections part II by Matteo Giardi
- Stiefel-Whitney classes as obstructions by Valentin Bosshard