Manuel Luethi HOMEPAGE

Manuel Luethi (a.k.a. Manuel Lüthi!)

I'm a mathematician with a specialization in dynamics, currently working as Oberassistent at ETHZ. I am broadly interested in satistical and machine learning, in particular in deep learning architecture design, and of quantitative methods ranging from inferential statistics to machine learning in health sciences, economics, and finance.

From September 2021 to February 2025 I was a PostDoc at EPFL under the guidance of Philippe Michel.

From October 2019 to September 2021 I was lucky to be a PostDoc at the Tel Aviv University working with Barak Weiss.

From March 2015 to October 2019 I did a PhD at ETHZ, where I also did my undergraduate studies. My advisor was Manfred Einsiedler.

For the period from October 1, 2018 to March 31, 2019 I visited the Einstein Institute of Mathematics at the Hebrew University enjoying an SNSF Doc.Mobility Fellowship.

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

Professional experience outside of mathematical research

I have (ongoing) experience as a data analyst and a software engineer in various sectors. 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, mostly for exploring applications of machine learning or for exploratory analysis of certain algorithms, e.g., the quality of approximation and rates of convergence for certain machine learning algorithms with known data generation mechanisms. This is part of my own learning experience. Some of the code can be found on my GitHub profile. The public repositories are all work in progress.

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., to appear.

Arxiv

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

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