Teaching

Quantum Mechanics for Mathematicians (Spring 2020)

• Course description in the catalogue

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:
  • Leon A. Takhtajan. Quantum Mechanics for Mathematicians, volume 95. American Mathematical Society, 2008.
  • Other reading suggestions

Symplectic Geometry and Hamiltonian Dynamics (Spring 2019)

• Course description in the catallogue

Materials:

• Syllabus and course plan
• List of Homework Exercises
• Notes:
  • Symplectic spaces and manifolds
  • Lagrangian submanifolds and symplectomorphisms
  • Symplectic rigidity and flexibility
  • Hamiltonian dynamics
  • Lagrangian dynamics and Legendre transform
  • Mechanical and magnetic Hamiltonian systems
  • Periodic orbits on a hypersurface
  • Contact type property
  • Contact geometry
• 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