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. In preparation.

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

About my non-mathematical activities

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. The public repositories 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