Teaching
"There is only one thing in the long run more expensive than education: no education." J. F. Kennedy.
"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.
Current Teaching at UW-Madison
Math 431, Introduction to the Theory of Probability.
Coorganising Math 921, the Graduate Analysis Seminar.
Upcoming Teaching at UW-Madison
Spring 2026: Math 376, Topics in Multi-Variable Calculus and Differential Equations.
Past Teaching
Lecturer for:
A 4-per-week lecture on Ergodic Theory for master students (summer semester 2025, at the University of Bonn); module: Advanced Topics in Number Theory. Click here for more information.
The lecture notes are here.
Final Exams: There will be oral exams on
i) 21 July, 22 July, and possibly 23 July
ii) 22 September, 23 September, and possibly 24 September.
Expectations for the Oral Exam:
The exam questions will be designed to assess conceptual understanding, rather than memorising details. The focus is on central theorems, their proofs, and consequences. While you might be asked to recall some definitions, this will play a minor role.
Only very short proofs would be asked to be presented in full. For longer proofs, a schematic outline might be requested. It would be best to answer the questions concisely so that more questions can be asked and answered.
Synopsis: The first part of the lecture 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 extremality of non-flat manifolds.
A 2h-per-week lecture on Decoupling and Applications for master students (winter semester 2024, at the University of Bonn); 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-per-week 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-per-week lecture on Probabilistic Number Theory (winter semester 2022, at Graz University of Technology) for master and PhD students; module: Elective subject Mathematics. See here.
Seminars conducted on:
A 2h-per-week seminar on Diophantine Approximation (summer semester 2024, at the University of Bonn) for master students; module: Graduate Seminar on Advanced Number Theory. See here.
A 2h-per-week graduate seminar on Determinant Methods for master students (winter semester 2024, at the University of Bonn). For more information, click here or 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)