# Teaching

"There is only one thing in the long run more expensive than education: no education." J. F. Kennedy.

Here is a collection of my teaching experience.

Upcoming Teaching (summer term 2025 at University of Bonn)

A 4h lecture on Ergodic Theory for master students; module: Advanced Topics in Number Theory. The first part will be a general introduction to Ergodic Theory (Birkhoff's Ergodic theorem, mixing, etc.). The second part will focus on applications in metric number theory. In particular, we discuss Diophantine approximation on manifolds and quantitative non-divergence in the space of lattices. This includes, but is not limited to, the beautiful work by Kleinbock and Margulis on the extremity of non-flat manifolds.

Current Teaching (winter term 2024 at University of Bonn)

A 2h lecture on Decoupling and Applications for master students; module: Selected Topics in Number Theory. The notes are here. For more information, click here. The content of the course centres around decoupling for the moment curve, and the paraboloid. As applications we discuss Vinogradov's Mean Value Theorem, and bounds on exponential sums. If time allows, we explain local smoothing for the wave equation.

A 2h graduate seminar on Determinant Methods for master students. For more information, click here.

For relevant details - modalities, prerequisites, topics - click here. The schedule is here.

We will study (a subset of) the following manuscripts.

a) Huxley's paper on rational points close to planar curves using Swinnerton-Dyer's determinant method.

b) Bombieri, and Pila's work on integer points on planar curves using their determinant method.

c) Marmon's paper on counting rational points on certain varieties using Heath-Brown's determinant method.

d) Heath-Brown's work on counting rational points near certain varieties using his approximate determinant method.

Past Teaching

Lecturer for:

A 2h lecture on Counting Rational Points on and near Manifolds (winter semester 2023, at University of Bonn) for master students; module: Selected Topics in Number Theory. Click here to access the lecture notes.

A 3h lecture on Probabilistic Number Theory (winter semester 2022, at Graz University of Technology) for master and PhD students; module: Elective subject Mathematics. See here.

Seminar conducted on:

A 2h seminar on Diophantine Approximation (summer semester 2024 at University of Bonn) for master students; module: Graduate Seminar on Advanced Number Theory. See here.

Exercise Classes/Teaching Assistant for:

Analytic Geometry (at University of Würzburg; 1 time)

Analysis I (at University of Würzburg; 1 time)

Analysis II (at University of Würzburg; 1 time)

Mathematics C (at Graz University of Technology; 3 times)

Corrected student homework sheets for:

Analysis I (at University of Würzburg; 1 time)

Analysis II (at University of Würzburg; 1 time)

Linear Algebra I (at University of Würzburg; 1 time)

Introduction to Algebra (at University of Würzburg; 1 time)

Number Theory (at University of York; 1 time)