About me
I am Eloi Martinet, a postdoctoral researcher at the University of Würzburg and part of the team of Mathematics of Machine Learning. I am interested in using a variational approach to tackle machine learning problems, and using neural networks capabilities to solve shape optimization problems.
In October 2023, I defended my PhD Thesis about spectral shape optimization supervised by Dorin BUCUR and Edouard OUDET. You can download the manuscript here.
You can download my CV here.
Education

Postdoc in Variational Methods in Machine Learning.
JMU (Würzburg, Germany)
PhD in Spectral Shape Optimization, 20192023 
Agrégation de Mathématiques, 20202021
Institut Fourier (Grenoble) 
Engineering School in Informatics and Applied Mathematics, 20162019
ENSIMAG (Grenoble)
LAMA (Chambéry), LJK (Grenoble)
Research interests
 Shape and topology optimization
 Numerical methods
 Level set method
 Machine Learning
Teaching
 20242025 : Lectures and exercise session of Mathematical Foundations of Data Science, JMU (Würzburg)
 20242025 : Seminar of Introduction to Data Science, JMU (Würzburg)
 2024 : Seminar of Machine Learning on Graphs, JMU (Würzburg)
 2024 : Working Group on FEM and the use of Neural Networks as PDE solver, JMU (Würzburg)
 2022  2023 : tutoring of practical sessions of numerical analysis, ENSIMAG (Grenoble)
 2022  2023 : tutoring of practical sessions of integration and Fourier transform, ENSIMAG (Grenoble)
 2021  2022 : course + tutoring of practical sessions of basic analysis, UGA (Grenoble)
 2019  2020 : tutoring of practical sessions of numerical analysis, USMB (Chambery)
Supervision
 2024 : Cosupervison of the MSc Internship of Nicolas Roblet with Romain Joly titled Spectrum of unbounded operators and applications to PDEs (report).
Publications
& preprints
Sharp inequalities for Neumann eigenvalues on the sphere
(2024),
with D. BUCUR and M. NAHON, Journal of Differential Geometry (to appear). 
Numerical optimization of Neumann eigenvalues of domains in the sphere
(2024),
Journal of Computational Physics. 
Maximization of Neumann eigenvalues
(2023),
with D. BUCUR and E. OUDET, Archive for Rational Mechanics and Analysis.
Research Projects
Optimization of Neumann eigenvalues in the plane
What is the shape of the drum that has the largest eigenfrencies ? We investigate this issue by implementing some densitybased optimization procedure.
Optimization of Neumann eigenvalues on the sphere
While the planar case has been investigated theoretically since the 50's, the optimization of Neumann eigenvalues on the sphere is still mysterious. We try to identify numerically some behaviour of the optimal densities.
Optimization of Neumann eigenvalues on the sphere
We perfom an analysis of the shape optimization problem of Neumann eigenvalues for domains on the sphere thanks to the level set method.
Teaching ressources
Numerical Methods for PDEs
From the Finite Element Method to Neural Networks
Exploring old and recent ways to solve PDEs. Given at the University of Würzburg in the summer semester of 2024.
Go to the courseOther Projects
Optimization of Neumann eigenvalues with FreeFem and Python
I provide the source code and some practical explanations on the density optimization of Neumann eigenvalues using python and FreeFem++.
A phasefield demonstration of the isoperimetric problem
The legendary isoperimetric problem is the most famous and ancient problem in shape optimization. It consists in finding the shape minimizing its perimeter while keeping its volume fixed. Here we simulate the solution to this problem using a relaxed formulation of the perimeter.