Rencontre avec les doctorants de l’Université du Luxembourg du 19 au 21 Novembre

Date/heure
19 novembre 2025 - 21 novembre 2025
Toute la journée

Oratrice ou orateur

Catégorie d'évènement
Doctorants

Site web de l’évènement.
Programme du 1er jour – Salle de conférence :

• • 13h30 – 14h15 : Exposé de Benjamin Florentin – IECL
    
    Can one hear the shape of a Steklov drum ?

    Introduced at the beginning of the 20th century, the Steklov eigenvalue problem has attracted growing interest in spectral geometry over the last few decades and remains a major research topic in the field. In this talk, we will focus on the associated spectral inverse problem consisting in recovering a metric of a compact Riemannian manifold with boundary from knowledge of its Steklov spectrum, or equivalently the spectrum of its Dirichlet-to-Neumann map (DN map). In other words, can one hear the shape of a “ Steklov drum ” ? We will present some recent positive results obtained on a certain class of manifolds with negatively curved boundaries.

• • 14h15 – 15h00 : Exposé de Marie Abadie – Université du Luxembourg
    
    Hyperbolic surfaces and graphs

    The goal of this talk is to provide a brief overview of the interactions between hyperbolic surfaces and certain combinatorial objects. A given surface has a large space of hyperbolic metrics, called its Teichmüller space, which itself admits a natural metric, called the Weil-Petersson (WP) metric. Distances between two hyperbolic metrics with respect to this WP metric are hard to compute. We will describe Brock’s combinatorial approach for approximating that distance using the graph of pair-of-pants decompositions.

• • 15h00 – 15h30 : Pause café en salle 113

• • 11h10 – 11h50 : Exposé de Aurélien Minguella – IECL
    
    A brief introduction to stochastic partial differential equations.

    Stochastic partial differential equations (SPDEs) are the mathematical objects used
    to describe the random dynamics of infinite-dimensional objects. They take applications in a
    broad range of areas, from statistical and theoretical physics, to fluid mechanics. These objects
    display very rich mathematical behaviour and have known a gain of interest since Martin Hairer
    was awarded the Fields medal in 2014 for constructing a solution theory for a very broad class
    of parabolic singular equations, namely regularity structures. Staying far away from regularity
    structures, we will try to give a quick overview of some simple SPDEs, but where some
    essential phenomena already arise. Some emphasis will be given on the invariant measures for
    such equations. We will first give a review of basic stochastic calculus and continue with an
    example of a linear SPDE: the stochastic heat equation. If time permits, we will have a glimpse
    of the complications happening in the non-linear case. We will finish with an informal overview
    of the most recent theories and current challenges in the field.

• • 16h15 – 17h00 : Exposé de Alexandre Benoist – Université du Luxembourg
    
    The ternary cyclotomic polynomials $\Phi_{3pq}$

    Cyclotomic polynomials are a classical and fundamental topic in number theory, and still an active field of research. The aim of this talk is introducing results about the coefficients of cyclotomic polynomials. I will first speak about the family of binary cyclotomic polynomials, which is completely understood. Then, I will move on ternary cyclotomic polynomials. I will provide a formula for computing the coefficients of the ternary cyclotomic polynomials of the form $\Phi_{3pq}$, from which we can derive various properties and solve conjectures for this family.

Programme du 2ème jour – Amphi 8 :

• • 9h15 – 10h00 : Exposé de Carl-Fredrik Lidgren – Université du Luxembourg
    
    Reconstructions, complete invariants, and anabelian geometry.

    In topology, a basic invariant of interest is the fundamental group of a topological space. As an invariant, this is useful for distinguishing between two topological spaces, but is in general not useful for determining that two spaces are the same because radically different topological spaces can have the same fundamental group. In algebraic geometry, on the other hand, one can define an arithmetic analogue of the fundamental group, also related to absolute Galois groups in number theory, which turns out to be considerably more rigid. The aim of the talk is to discuss this phenomenon and the area which studies it: anabelian geometry.

• • 10h00 – 10h30 : Pause café, Hall de l’amphi 8

• • 10h30 – 11h15 : Exposé de Vidhi Vidhi – IECL
    
    Statistical approach for quantifying the evolution of tumor heterogeneity in chronic
    lymphocytic leukemia (CLL).

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• • 11h15 – 12h00 : Exposé de Tim Seuré – Université du Luxembourg
    
    Balancing Powers

    This talk explores surprising equalities between power sums arising from a
    binary-based partition of the integers.

• • 12h00 – 13h30 : Déjeuner

• • 9h15 – 10h00 : Exposé de Amine Iggidr – IECL
    
    From noise to harmony: Understanding the primes through waves

    Prime numbers appear scattered randomly along the integers, yet their distribution hides some sort of structure. This talk introduces how Fourier analysis ideas reveal periodic components inside the primes. This help us explain classical phenomena such as Chebyshev’s bias and reveal why complex zeros of L-functions govern the oscillations in prime-counting functions. In this talk we trace the historical development from Dirichlet to modern analytic number theory and show how harmonic analysis serves as a powerful tool which helps us understand the secrets of prime numbers.

• • 14h15 – 15h00 : Exposé de Lucia Celli – Université du Luxembourg
    
    Wide neural networks with general weights: convergence rate and explicit dependence on the hyper-parameters.

    Wide fully connected neural networks converge at initialization to a Gaussian process, but quantitative rates are not well understood. I present explicit, non-asymptotic bounds for this convergence in both one- and multi-dimensional settings under general weight assumptions. The results make all dependencies on depth, width, activation, and moments explicit, covering common cases such as ReLU and Gaussian initialization, and clarify when the limiting covariance remains non-degenerate.

• • 15h00 – 15h30 : Pause café, Hall de l’amphi 8

• • 15h30 – 16h15 : Exposé de Hugo Nouaille – IECL
    
    Rough paths: Integration beyond smoothness.

    Almost every theory of integration applies to solving certain ODE or PDE problems. We review some Cauchy problems with Hölder signals and their formulation in integral form. From there, we can observe how the idea of rough paths is motivated. Finally, we will try to provide some intuition about one object of this theory: the rough integral.

• • 16h15 – 17h00 : Exposé de Leolin Nkuete – Université du Luxembourg
    
    Hopf Galois extensions

    It is well known that for any Galois extension L/K one can associate an arithmetic object G:=Gal(L/K) called the Galois group of the extension L/K. This group gives rise to a group algebra H=K[G], which, is in particular a Hopf algebra. We called this group algebra a Hopf Galois structure associated with the extension L/K. The goal of this talk is to explain how this framework can be generalized to non-Galois extensions.

• • 19h30 : Dîner au Grand Café Foy (1 Pl. Stanislas, 54000 Nancy)

Programme du 3ème jour – Amphi 8 :

• • 8h30 – 9h15 : Petit déjeuner, Hall de l’amphi 8

• • 9h15 – 10h00 : Exposé de Simon Bartolacci – IECL
    
    Global Waiting: An Alarm Clock Optimization Perspective.

    What time should I set my alarm tomorrow morning? Like many, I have often
    wondered about this. And like many I first turned to deterministic constrained optimization
    theories, involving Lagrange multipliers and other classical tools. I soon realized that I cannot
    know exactly whether there will be traffic, at what time my colleagues will arrive, or whether I
    might fall back asleep after the first alarm. The optimization problem underlying this question
    is therefore inherently stochastic.
    While I cannot predict the future, I do have empirical knowledge: I frequently oversleep, often
    leave so late that I avoid traffic, and sometimes arrive well after my colleagues. This gives me
    an empirical understanding of phenomena whose laws I do not know. Can optimizing over such
    empirical phenomena lead to a truly optimal alarm time? This is precisely the kind of problem
    studied in stochastic optimization, and this talk will discuss the answer.
    Moreover, focusing solely on expected outcomes is not ideal: my primary concern is not just
    the average timing but reducing the risk of missing critical events, such as the coffee break. By
    incorporating risk measures beyond the expectation, stochastic optimization allows us to design
    alarm strategies that are robust to worst-case scenarios and better aligned with practical
    priorities.

• • 10h30 – 10h30 : Pause café, Hall de l’amphi 8

• • 10h30 – 11h15 : Exposé de Francesca Pistolato – Université du Luxembourg
    
    From Galton board to Fractional Brownian motion.

    In this talk, we will explore how simple experiments can illustrate fundamental ideas in probability. We revisit the Central Limit Theorem through the Galton board and then extend the intuition to fractional Brownian motion, highlighting how randomness can exhibit memory and long-range dependence.

• • 10h30 – 11h15 : Exposé de Kilian Lebreton – IECL
    
    Probabilistic approach to certain sums arising from number theory.

    Kloosterman sums, Gauss sums, Birch sums are examples of families of sums of fonctions \(\varphi : (\mathbb{Z}/n\mathbb{Z})^* \to \mathbb{U}_n \), where \(\mathbb{U}_n \) denotes the set of \(n\)-th roots of unity. They arise naturally in number theory. Once normalized by \(\sqrt{n} \), the complete sums (within their respective families) behave like bounded random variables. From this, we can deduce that their partial sums converge in law to a random Fourier series, that short sums converge to a Gaussian distribution, and that we can estimate the maximum of their partial sums.