Bachelor and master projects topics

You can find below different ideas. Feel free to contact me, I am open to discuss alternative ideas.

• Discrete dynamical systems
  • Number and spectral theory of Gauss and Farey maps
  • Laws of extreme events for random dynamical systems
  • Using Markov chains with constraints to optimize cloud application distribution
• Spectral theory (analytical approach)
  • Modified Hofstadter butterflies in the chequerboard Harper model
  • Semiclassical analysis
• Spectral theory (geometric approach)
  • Quantum chaos and magnetic billiards (of finite and infinite measure)
  • Spectral sub-Riemannian geometry and the Ahronov-Bohm effect
  • The bicycle problem in contact geometry
• Numerical methods and programming
  • Design and implementation of differential equations solvers interface in Owl, the OCaml scientific framework
  • Taylor and geometric numerical solvers in OCaml and Owl, the OCaml scientific framework, in particular
  • Design and implementation of numerical root finding interface in Owl, the OCaml scientific framework

Former students

• Daniel Boutros: Mathematical aspects of the Feynman path integral (2020) [link]
• Jochem Loedeman: The Geometry of Attractors in Inflationary Cosmology (2019) [link]
• Jonathan Pim: On Yoshida's Method For Constructing Explicit Symplectic Integrators For Separable Hamiltonian Systems (2019) [link]
• Bas de Pooter: Geodesic Flow of the Modular Surface and Continued Fractions (2019) [link]
• Rick van Voorbergen: On the extension of Lie algebras using double extensions and Lie algebra expansions (2019) [link]
• Kenzo Yasaka: Spectral almost-Riemannian geometry and the magnetic Aharonov-Bohm effect (2020) [link]

2020/2021

• Analysis on Manifolds - period 1b
  Project Chaos Theory (with H. Jardon) - period 1b
• Hamiltonian Systems (master) - period 2a

Past

2019/2020

• Calculus for Chemistry - period 1a
  Partial differential equations (with A. Waters) - period 1a
• Hamiltonian Systems (master) - period 2a (Lecture Notes)

Some links are broken. They will be fixed once I rewrite and reorganize this page.

• Linear algebra and multivariable calculus for Chemistry (with P. Kilicer) - period 1b
• Partial differential equations (with A. Waters) - period 1b
• Geometry - period 2b
• Introduction to C++ (Reading, enhancement week) - 2015/2016 Lecture Notes
• Introduction to Python (Reading, enhancement week) - 2015/2016 Interactive Lecture Notes
• Spectral Theory (MATHM111) - 2014/2015 Linear Operators and Their Spectra (on Prof. E. B. Davies homepage)
• Mathematics for Science 1 (MATH6105) - 2013/2014

For the complete teaching experience refer to my CV.