Manuel Luethi HOMEPAGE

Manuel Luethi (a.k.a. Manuel Lüthi!)

I'm a mathematics PhD and former economist specializing in homogeneous dynamics and dynamical systems with a focus on applications to number theory. My research covers questions about measure rigidity for random walks, higher rank diagonalizable flows, and horospherical actions. It combines a wide range of techniques from dynamical systems, ergodic theory, probability theory, information theory, functional analysis, algebraic groups, and geometry.

In addition to my research, I'm experienced in software development for the banking sector and with statistical analysis of financial, ecological, and clinical data. I'm generally interested in the development and application of software solutions and quantitative methods in settings requiring high degrees of accuracy and offering a serious challenge, e.g., risk modelling, medical and outcome research, health care, and finance.

I am experienced in inferential statistics, am working with parametric models, non-parametric models, and other machine learning techniques, e.g., calibration of SDEs via (deep) neural networks. I have some particular interest in deep operator learning, targeted learning, and interpretable machine learning.

From October 2019 to August 2025 I worked as an independent researcher funded by the SNF and the ISF at Tel Aviv University, EPFL, and ETHZ. I have collaborated across the globe and published various works in collaboration with Menny Aka, Manfred Einsiedler, Osama Khalil, Taylor McAdam, Philippe Michel, Nimish Shah, Barak Weiss, and Andreas Wieser.

For more details, you can find a curriculum vitae here.

Mathematical Research

Measure rigidity and fractals.

Joint with Osama Khalil and Barak Weiss. Submitted to GAFA.

Talk at IHP Arxiv

Quantitative disjointness.

Joint with Menny Aka, Manfred Einsiedler, Philippe Michel, and Andreas Wieser. In preparation.

Random walks, spectral gaps, and Khintchine's theorem on fractals.

Joint with Osama Khalil. Invent. Math.

PDF Published

Simultaneous supersingular reductions of CM elliptic curves.

Joint with Menny Aka, Philippe Michel, and Andreas Wieser. J. Reine Angew. Math.

Published

Primitive rational points and higher powers on expanding horocycles in the modular surface.

Joint with Manfred Einsiedler and Nimish Shah. Ergod. Theory Dyn. Syst.

Arxiv Published

Effective equidistribution of primitive rational points on expanding horospheres in Hilbert modular surfaces.

J. Number Theory.

Arxiv Published

Kloosterman Sums, Disjointness, and Equidistribution.

Joint with Manfred Einsiedler. In: Ferenczi S., Kułaga-Przymus J., Lemańczyk M. (eds) Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 2213. Springer, Cham

Chapter Book

Coding

Most of the code I produce(d) can not be made publicly available. Whenever I find the time, I do some coding on the side. Some of the code can be found on my GitHub profile. If there are public repositories, they are all work in progress and form part of my learning experience.

Miscellaneous notes and other articles

Reflections on diverse and inclusive teaching.

Joint with Meike Akveld. In: ETH Learning and Teaching Journal, vol. 3, no. 1, 36-44 (2022)

Article Journal

Self-assessment in student seminars in mathematics.

Joint with Andreas Wieser. In: ETH Learning and Teaching Journal, vol. 1, no. 2, 49-57 (2020)

Article Journal

A motivated proof of the singular value decomposition

A proof of the singular value decomposition avoiding matrices in order to give a better geometric motivation. A write up of the proof provided in this course on Linear Algebra by Meike Akveld.

PDF

A genuinely linear proof of joint diagonalizability

A proof avoiding the minimal polynomial of the fact that a family of commuting, diagonalizable matrices is jointly diagonalizable. A reorganized write up of the sample solution to an exercise posed in this course on Linear Algebra by Meike Akveld.

PDF

Teaching Experience

Spring 2025
Lecturer for Dynamical Systems and Ergodic Theory .
Autumn 2024
Lecturer for Algebraic Number Theory .
Spring 2023
Lecturer for Algebraic Number Theory .
Winter 2022
Lecturer for Introduction to Analytic Number Theory joint with Petru Constantinescu
Spring 2022
Lecturer for Algebraic Number Theory .
Winter 2021
TA for Algèbre linéaire avancée I .
Spring 2019
Lecturer for student seminar on Primes of the form x2+ny2 Joint with Menny Aka and Andreas Wieser .
Spring 2018
Lecturer for student seminar on Homogeneous dynamics and counting problems . Joint with Andreas Wieser .
Other teaching experience.
In addition, during my PhD at ETHZ, I was the coordinator for the first year course in linear algebra (Autumn 16, Spring 17, Autumn 17, Spring 18), which involves preparation of the exercises, the exams and the solutions as well as organization of the respective events. I was also coordinating a one year course on Lie groups and their unitary representations (Autumn 15, Spring 16). Previously, I was a teaching assistant in Functional Analysis II.

Bookshelf

Like most people, I like to share what brings me joy, which in my case leads to recommendations on music, both for listening as well as playing (on the violin), cycling and hiking routes, and texts. So here I list some of the texts that I found particularly interesting and enjoyable. For the experts in their field, each recommendation is obvious. Most of them are chosen because I find them excellently written. There isn't any point in me compiling a list of most important texts from various areas.

G.A. Akerlof. "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism." Q. J. Econ. 84 (3) 488–500, 1970. Link
K.J. Arrow. "A Difficulty in the Concept of Social Welfare." J. Political Econ. 58 (4) 328–346, Aug. 1950. Link
G. Becker. "Crime and Punishment: An Economic Approach." J. Political Econ. 76 (2) 196–217, Mar.–Apr. 1968. Link
A. Borel. "Introduction aux groupes arithmétiques." Hermann, 1970.
L. Breiman. "Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author)." Statist. Sci. 16 (3) 199–231, Aug. 2001. Link
L. Breiman. "Probability." [Corrected republication 2nd printing], Society for Industrial and Applied Mathematics, 1993.
D. Celentano et al. "Gordis Epidemiology." Seventh edition., Elsevier, 2026.
R. Coase. "The Problem of Social Cost." J. Law and Econ. 3 (1) 1–44, 1960. Link
W. Easterly. "The White Man’s Burden: Why the West’s Efforts to Aid the Rest Have Done so Much Ill and so Little Good." New York, 2006.
M. Einsiedler and friends. I find every single one of his books excellent. Look at the list here
A. Eskin and C. McMullen. "Mixing, counting, and equidistribution in Lie groups." Duke Math. J. 71 (1) 181–209, July 1993. Link
S. Hustvedt. "The Summer without Men." Sceptre, 2011.
Sh. Jackson. "The Haunting of Hill House." Penguin Books, 2009.
F. Modigliani and M. Miller. "The Cost of Capital, Corporation Finance and the Theory of Investment." Am. Econ. Rev. 48 (3), 261–297, 1958. Link
B. Øksendal. "Stochastic Differential Equations: An Introduction with Applications." 6th ed., 5th. corr. print., Springer, 2010.
J.-P. Serre. "A Course in Arithmetic." Graduate Texts in Mathematics, Vol. 7. Springer-Verlag New York Inc. 1997. Link
P. Walters. "An Introduction to Ergodic Theory." Graduate Texts in Mathematics, Vol. 79. Springer-Verlag New York Inc. 1982.