# Teaching

## 2020

I am not teaching this year.

## Previous activities

During the academic year 2018-2019 Jennifer-Jayne Jakob and I organized the graduate seminar "What's so cool about..?" where professors give talks explaining what's "cool" their research. See this link for the speakers in the spring semester.

Here is a selection of other teaching activities of mine (see my CV for a more complete list):

- Teaching assistant for commutative algebra taught by Emmanuel Kowalski.
- Teaching assistant for a seminar taught by Manfred Einsiedler. Note that this is a continuation of the course Functional analysis II in Spring 2019.
- Spring 2019: I organized the seminar "Primes of the form $x^2+ny^2$" with Menny Aka and Manuel Luethi that roughly treated the first half of D.A. Cox' book with the same title.
- Fall 2018 and Spring 2019: teaching assistant for Functional analysis I and Functional analysis II by Manfred Einsiedler writing exercise sheets and solutions.
- Spring 2018: I organized the seminar "Homogeneous Dynamics and Counting Problems" with Manfred Einsiedler and Manuel Luethi.
- Spring 2017: I organized the seminar "Arithmetic of Quadratic Forms" with Menny Aka following the book of Cassels with the same title.

## Lecture notes and other writings

** Feedback and self
-assessment in undergraduate student
seminars in mathematics ** with Manuel Luethi, ETH Learning and Teaching Journal, Vol 2, No 1, 2020.

Abstract: " In this article we will discuss bachelor’s seminars in mathematics at ETH. Most students (in these seminars) are neither used to individually preparing material from textbooks nor to discussing advances mathematics with fellow students. As these seminars usually follow a single thread, it is often impossible to quickly catch up on the content of past lectures. Hence there is also the risk that students only focus on their own talks, which often results in badly aligned talks. To overcome these problems, we implemented two tweaks to the standard setup. These are extensive meetings with the organizers and few mandatory exercises. We will evaluate the success of these measures and, where success is scarce, propose further measures to possibly address these problems."

These are extensive lecture notes in german written by Manfred Einsiedler and myself (with additions by Peter Jossen) for the first year course in analysis at ETH Zurich. They were in particular used in the academic years 2016-2017 (see this link) and 2017-2018 (see this and this link). The topics covered are roughly the following:

- Introduction to logic and set theory.
- Real numbers, continuity.
- Riemann integral for functions in one variable.
- Sequences, convergence, series, power series.
- Differential calculus for functions in one variable, the fundamental theorem of calculus.
- Metric spaces.
- Differential calculus for functions in several variables.
- Implicit function theorem, inverse function theorem and an introduction to differential geometry (submanifolds of $\mathbb{R}^n$ and Lagrange multipliers).
- Riemann integral for functions in several variables.
- Path and surface integrals, Gauss' Theorem and Stokes' Theorem.
- Ordinary differential equations.

** What is... the shape of a lattice?**

These are colloquial notes for a talk I give in the "What is...?"-seminar of the Zurich Graduate School of Mathematics.

** On the "Banana"-Trick of Margulis **

Short and very preliminary notes explaining the thickening trick developed by G.A. Margulis in a specific instance. These were used in the seminar "Homogeneous Dynamics and Counting Problems" mentioned above.

** Arithmeticity of lattices in higher rank real groups **

Preliminary notes for a talk I gave in an informal reading course in Zurich, fall 2019. The aim of these notes is to deduce arithmeticity of lattices in higher-rank real groups from Margulis' superrigidity result.