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

2020/2021

• Analysis on Manifolds - period 1b

  Project Chaos Theory - 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

  Syllabus | Q&A forum and exercises (on UCL Moodle)
  Linear Operators and Their Spectra (on Prof. E. B. Davies homepage)

• Mathematics for Science 1 (MATH6105) - 2013/2014

  Syllabus | Lecture notes, Q&A forum and exercises (on UCL Moodle)

For the complete teaching experience refer to my CV.