Teaching

Lectures and Seminars

Spring 24: Seminar Elliptic Functions and Modular Forms

Fall 23: Seminar Elliptic Curves
Spring 23: Lecture Elementary Number Theory
Spring 22: Lecture Elliptic Functions
Fall 21: Seminar L-functions
Fall 21: Seminar Modular Forms
Fall 20: Seminar Elliptic Curves
SS19: Lecture Modular Forms

Thesis supervision

Master's theses

Johannes Buck - Eisenstein series for the Weil representation and theta series (2016)
Paul Kiefer - Eisenstein series and automorphic forms of singular weight (2017)
Jennifer Kupka - Mock modular forms and traces of singular moduli (2017)
David Klein - Ramanujan's mock theta functions and harmonic Maass forms (2018)
See also the research paper by David Klein and Jennifer Kupka, which is based on their Master's theses.
Suleman Khalil - Vector valued modular forms for the Weil representation (2019)
Maximilian Müller - On the converse theorems of Hecke and Weil (2019)
Carolin Berke - Fourier coefficients of meromorphic modular forms (2020)
Pauline Scharf - Relations for Hurwitz class numbers (2021)
Edward Brunner - The theory of complex multiplication (2021)
Kai Badinski - Non-holomorphic Eisenstein series for the Weil representation (2021)
Baptiste Depouilly - The Kudla-Millson theta lift (2021)
Edoardo Mazzoni- Locally harmonic Maass forms and meromorphic modular forms (2022)
Stefan Moser - Congruent numbers and Tunnell's Theorem (2022)
Fabian Roshardt - Meromorphic Hilbert modular forms (2023)
Cyrill Graf - Cycle integrals of the j-function and mock modular forms (2024)
Lorenzo Mombelli - Derivatives of L-functions of Eisenstein series and Fourier coefficients of harmonic Maass Eisenstein series (2024)
Aline Isenschmid - Explicit formulas for the partition function (2024)

Bachelor's theses

Paul Kiefer - Hecke characters and theta series for imaginary quadratic fields (with J.H. Bruinier 2015)
Suleman Khalil - Poincaré series with cut-off functions (with J.H. Bruinier 2015)
Joschka Braun - Class invariant for certain non-holomorphic modular functions (with J.H. Bruinier 2016)
Saskia Woznik - Maass forms and invariant differential operators (with J.H. Bruinier 2017)
Matthias Storzer - Growth estimates for the Fourier coefficients of cusp forms (with J.H. Bruinier 2017)
Michelle Möll - Representation numbers of binary quadratic forms (2017)
Kristina Rolinger - Binary quadratic forms and quadratic number fields (2020)
Edoardo Mazzoni - Eta products (2021)
Karlo Jerkovic - Periods of modular forms and the Theorem of Manin (2022)
Golo Wolff - Elliptic curves and the Congruent Number Problem (2023)
Leopold Karl - On the finiteness of simple eta-quotients of fixed level or fixed weight (2024)
Jonas Menzi - Sums of three and four squares (2024)
Janine Roshardt - The Dirichlet Class Number Formula (2024)

Semester papers

Baptiste Depouilly - Recurrence formulae for the coefficients of mock theta functions of order 7 and 5 (2021)
Xiao Yang - Poincaré series related to periods of modular forms (2021)
Ana Marija Vego - Traces of singular moduli (2022)
Filip Kovacevic - Modular forms with rational periods (2022)
Ryan Rueger - Eta products (2023)
Edoardo Mazzoni - Derivatives of L-functions of Eisenstein series and mock modular forms (2023)
Jonas Kramer - Quadratic forms and number fields (2023)
Ryan Rueger - Taylor expansions of modular forms at CM points (2023)

Summer schools for high school students

I organized some courses in summer schools for high school students at ETHZ and TU Darmstadt. The summer schools aim at students aged between 14 and 19 who are particulary interested in mathematics.

In 2024, Ryan Rueger and I supervised a course on The Oddities of Infinity in the annual Studienwoche at ETHZ. We discussed Hilbert's Hotel and the notions of countable and uncountable sets, studied interesting sequences and series, and investigated classical paradoxa of infinity. For example, we constructed the Leaning Tower of Lire, a block-stacking tower which can have an arbitrary long overhang, and we discussed the painter's paradox, also known as Gabriel's horn, which is an infinitely long 'horn' that can be filled with a finite amount of paint, but cannot be painted with a finite amount of paint from the outside. Moreover, we introduced computable numbers and studied languages accepted by finite state machines.

In 2022 and 2023, together with Alessandro Lägeler and Patrick Amrein we organized a course on Cryptography and Number Theory in the annual Studienwoche at ETHZ. We discussed some classical encryption schemes such as the Caesar Cipher and how they can be broken, but also the RSA algorithm and its number theoretical foundations.

In 2018, Julian Bitterlich and I gave a course on Computability Theory during a summer school for high school students at TU Darmstadt. The summer school has been organized annually since 2014 by Anna von Pippich and Fabian Völz. In addition to three lectures on the basics of the theory of computation we built a real life Turing machine together with the seven students attending our course. The machine was inspired by the original Turing machine by Jeroen van den Bos and Davy Landman, which they built for an exhibition in celebration of the Alan Touring Year 2012.

In 2016, Fabian Völz and I supervised a course on The Oddities of Infinity in the annual summer school organized by Anna von Pippich and Fabian Völz at TU Darmstadt.

Lego Turing Machine

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