## About

9

Publications

409

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39

Citations

Introduction

I do research AI, specializing in Computer Vision, in Pure Mathematics, specializing in Dynamical Systems, and in Numerical Analysis for Civil Engineering, specializing in Dynamics of Structures

Additional affiliations

September 2019 - March 2020

**Shift Technology**

Position

- Researcher

Description

- I did research in AI and Machine Learning as part of Shift Technology's research team, specializing in computer vision applied in fraud detection and related problems in the insurance industry

September 2018 - August 2019

**Université des Sciences et Technologies de Lille**

Position

- PostDoc Position

Description

- Research on aspects of KAM theory and cohomology of dynamical systems

## Publications

Publications (9)

In this m\'emoire we study quasiperiodic cocycles in semi-simple compact Lie
groups. For the greatest part of our study, we will focus ourselves to
one-frequency cocyles. We will prove that $C^{\infty}$ reducible cocycles are
dense in the $C^{\infty}$ topology, for a full measure set of frequencies.
Moreover, we will show that every cocycle (or an...

We continue our study of the local theory for quasiperiodic cocycles in
$\mathbb{T} ^{d} \times G$, where $G=SU(2)$, over a rotation satisfying a
Diophantine condition and satisfying a closeness-to-constants condition, by
proving a dichotomy between measurable reducibility (and therefore pure point
spectrum), and purely continuous spectrum in the s...

We provide a general argument for the failure of Anosov-Katok-like constructions to produce Cohomologically Rigid diffeomorphisms in manifolds other than tori. A $C^{\infty }$ smooth diffeomorphism $f $ of a compact manifold $M$ is Cohomologically Rigid iff the equation, known as Linear Cohomological one, \begin{equation*} \psi \circ f - \psi = \va...

Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in $\mathbb{T}^{d}\times G$, $G$ a compact Lie group, over a Diophantine rotation. We then prove that if this rotation vector is Diophantine with respect to the rotation in $\mathbb{T}^{d}$, the cocycle is smoothly redu...

We prove that if the frequency of the quasi-periodic $\mathrm{SL}(2,\R)$ cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1}{2}<\kappa<1$, the Lyapunov exponent is exactly $\kappa$-H\"older continuous; the extended eigenstates of the potential have optimal sub-linear growth; and the dual oper...

Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in $\mathbb{T}^{d} \times G$, $G$ a compact Lie group, over a Diophantine rotation. We then prove that if this rotation vector is Diophantine with respect to the rotation in $\mathbb{T}^{d}$, the cocycle is smoothly red...

We prove a theorem asserting that, given a Diophantine rotation $\alpha $ in a torus $\mathbb{T} ^{d} \equiv \mathbb{R} ^{d} / \mathbb{Z} ^{d}$, any perturbation, small enough in the $C^{\infty}$ topology, that does not destroy all orbits with rotation vector $\alpha$ is actually smoothly conjugate to the rigid rotation. The proof relies on a K.A.M...

We prove local genericity of Distributional Unique Ergodicity (DUE) for
certain classes of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$,
extending and/or refining some preceding results in the field. We then derive
some consequences for one-frequency cocycles. We also confirm in this context
(and, therefore, in a manifold of dimension $...

We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times
G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the
assumption that the rotation in the basis satisfies a Diophantine condition. We
prove differentiable rigidity for such cocycles: if such a cocycle is
measurably conjugate to a constant one satisf...