I enjoy learning mathematics for its own sake, but I typically also have concrete applications in mind.

During my bachelor and master studies I worked on PDEs, writing my Master's thesis on the analysis of semilinear wave equations via Young measures.

In my PhD I have mainly worked on nonparametric statistics, analysing variational estimators defined by total variation penalties and multiscale constraints. I proved that these estimators are minimax optimal for estimating functions of bounded variation in any dimension. Before that, no method was known to be minimax optimal for bounded variation functions in dimension d>1. The theoretical analysis relies strongly on harmonic analysis, and the efficient computational implementation uses techniques from nonsmooth optimization.

I'm currently interested in the theoretical analysis of optimization methods, and in the properties of deep neural networks applied to statistical problems.


I have mentored Bachelor and Master students in the following topics:

• Estimation in Semiparametric Mixture Models - from Algorithms to Asymptotics. Master's thesis by Markus Pohlmann, University of Göttingen, summer 2017-2018.
• Random forests for classification: theoretical analysis and simulations. Bachelor's thesis by Leo Claus Weber, University of Göttingen, 2019.
• Optimal estimation of transport maps. Master's thesis by Rupsa Basu, University of Göttingen, 2020-present.

I have also worked on the following applied projects:

• Institut Catalán de Nanotechnologia (with Dr. Adrian Bachtold; 2011-2012): electromechanical properties of carbon nanotubes.
• Massachusetts Institute of Technology (with Prof. Pablo Jarillo-Herrero; summer 2011): superconductivity in graphene.
• Max Planck Institute for Biophysical Chemistry (with Prof. Stefan Hell; 2014-2018): quantitative methods for nanoscale fluorescence microscopy.

Summer semester 2018:
Mathematical Statistics II, Exercises. Topics: confidence intervals, hypothesis testing.

Summer semester 2017:
Mathematical Statistics IV, Exercises. Topics: nonparametric regression.

Winter semester 2016/2017:
Mathematical Statistics III, Exercises. Topics: multiple testing, nonparametric regression.

CV_delAlamo.pdf

Publications

Total variation multiscale estimators for linear inverse problems

M. del Álamo,  and A. Munk
arxiv preprint - To appear in Information and Inference

Frame-constrained Total Variation Regularization for White Noise Regression

M. del Álamo, H. Li,  and A. Munk
arxiv preprint - To appear in The Annals of Statistics

The molecular contribution function in RESOLFT nanoscopy

Strong Coupling between Mechanical Modes in a Nanotube Resonator

A. Eichler, M. del Álamo Ruiz, J. A. Plaza, and A. Bachtold
Physical Review Letters 109, 025503 – Published 11 July 2012

 

PhD Thesis:

Multiscale Total Variation Estimators for Regression and Inverse Problems

Predicate: Summa cum laude. 2019 pdf