Felix Voigtlaender

Postdoctoral researcher in mathematics
at the Department of Scientific Computing
Catholic University of Eichstätt-Ingolstadt

Email: felix@voigtlaender.xyz
CV (last updated on 2 September 2018)


If you trust in yourself. . .and believe in your dreams. . .and follow your star. . . you'll still get beaten by people who spent their time working hard and learning things and weren't so lazy.

—Terry Pratchett, The Wee Free Men

Research interests

I am interested in Functional analysis and Harmonic analysis, in particular in
  • Function spaces and their embeddings
  • Multiscale systems (wavelets, shearlets and generalizations)
  • Banach frames and atomic decompositions
  • Neural networks and their properties, in particular their expressiveness and approximation properties
  • Coorbit theory
  • Approximation theory
  • Time-frequency analysis
  • Fourier analysis
As a mathematical hobby, I am interested in almost everything related to measure theory and in trying to crack toy problems like this one (which is solved by now).

Biography

I am currently a Postdoctoral researcher in the Scientific Computing Group at KU Eichstätt, part of the group of Götz Pfander.

I studied mathematics (Bachelor + Master) and computer science (Bachelor) at RWTH Aachen University, Germany, where I graduated with the Master degree with distinction in 2013.

As a Ph.D. student, I then joined the group of Hartmut Führ at RWTH Aachen University, where I studied the approximation theoretic properties of different multiscale systems. With my Ph.D. thesis 'Embedding Theorems for Decomposition Spaces with applications to Wavelet Coorbit Spaces', I graduated with distinction in November 2015. In November 2016, I was awarded the Friedrich-Wilhelm-Award 2016 for my thesis.

I highly enjoy teaching mathematics and am committed to explaining carefully and presenting the material in an enjoyable way. At RWTH Aachen University, I have been teaching assistant for Analysis I and III, and for Harmonic analysis. Therefore, I am very proud to have received the Teaching award of the student council of mathematics at RWTH Aachen University.

From April 2016 until January 2018, I was a postdoctoral researcher at TU Berlin in the group of Gitta Kutyniok, where I worked on the DEDALE project. As part of that project, and with support by Anne Pein, I developed the DEDALE α-shearlet transform.

Since February 2018, I am part of the Scientific Computing Group at KU Eichstätt.


News

15 September 2018

Update of the website and of the CV. Added several new preprints and talks.

8 April 2018

First update of the website since I moved from Berlin to Eichstätt. The CV is still out of date, however...

23 November 2017

After my talk about the approximation properties of ReLU neural networks at the Research seminar "Mathematics of Computation", I was asked for the slides to my talk. These can be found here.

Many thanks to Tino Ullrich for inviting me to give this talk!

23 September 2017

I just added to my list of publications two new preprints that I recently uploaded to the arXiv.

The first one establishes a rather general version of Price's theorem: It gives a simple formula for computing the partial derivatives of the map ρ ↦ 𝔼[g(Xᵨ)], where Xᵨ is a normally distributed random variable with covariance matrix ρ. Price published this result in 1958, but did not precisely state the required assumptions on g. In the paper, I show that one can in fact take every tempered distribution g. This result is used in the paper ℓ¹-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed? written by three of my colleagues.

The second preprint, written jointly with my colleague Philipp Petersen analyzes the approximation power of neural networks that use the ReLU activation function. We analyze how deep and wide such a neural network needs to be, in order to approximate any "piecewise smooth" function. We also show that these bounds are sharp.

I also added several talks that I gave in the last months, including the lecture notes for the lecture series "Sparsity Properties of Frames via Decomposition Spaces" that I gave at the Summer School on Applied Harmonic Analysis in Genoa.

09 February 2017

I just added a new preprint to my list of publications that I uploaded to the arXiv in December.

Furthermore, I am very happy to be a speaker at the Summer School on Applied Harmonic Analysis that will take place in Genoa from July 24-28, 2017.

Finally, I want to mention that my toy problem (about whether completeness of spaces can be characterized by the convergence of Neumann series) has been solved (negatively) quite a while ago.

28 July 2016

First version of this website was uploaded :)