PhD away days – Université du Luxembourg

Date/heure
20 mai 2026 - 22 mai 2026
09:00 - 18:00

Lieu
Luxembourg University

Oratrice ou orateur
PhD students from the two universities

Catégorie d'évènement
Séminaire des doctorants


Résumé

Wednesday 20/05 – MSA 2.240 :

    • 12:30 – 14:00 : Lunch + Poster Session
    • 14:00 – 14:45 : Talk

      Title
      Abstract
    • 14:45 – 15:30 : Rodolphe Abou Assali – IECL

      Steklov problems and spectral inequalities in planar domains
      Classical spectral problems, such as the Dirichlet and Neumann problems, focus on the analysis of eigenvalues and eigenfunctions with applications to heat conduction, sound propagation, and vibrational modes in domains with boundaries. Other well-known problems are the Steklov and biharmonic Steklov problems with various boundary conditions.
      Kuttler and Sigillito established fundamental inequalities relating the eigenvalues of these problems in planar domains. These results were later extended to the scalar case on Riemannian manifolds by Hassannezhad and Siffert. We recently generalized these inequalities to the setting of differential forms.
      In this talk, we present these spectral problems and the Kuttler-Sigillito inequalities in planar domains, and briefly discuss their generalization.
    • 15:30 – 16:00 : Break
    • 16:00 – 16:45 : Talk

      Title
      Abstract
    • 16:45 – 17:30 : Valentin Clarisse – IECL

      Title
      The Einstein equations are central to general relativity. They relate the geometry of spacetime to the distribution of matter within it.
      As we will see later, they form a particularly challenging system of partial differential equations to study. The first major breakthrough in mathematical relativity was achieved by Y. Choquet-Bruhat, who proved in 1952 the local-in-time existence of solutions to the Einstein equations viewed as an evolution problem.
      More recently, in 1993 and 1994, R. Gregory and R. Laflamme numerically demonstrated the instability of certain types of black string extensions in dimensions greater than or equal to $5$. In 2012, R.M. Wald and S. Hollands developed a fairly general method and criterion for studying the linear stability of black holes, which can be applied to establish Gregory–Laflamme-type instabilities.
      The article we will focus on, which is more accessible, comes from the doctoral thesis of Sam C. Collingbourne. It was submitted in 2020 and is entitled The Gregory-Laflamme Instability of the Schwarzschild Black String Exterior. It provides a direct mathematical proof of the Gregory–Laflamme linear instability in dimension $5$.

Thursday 21/05 – MSA 2.240 :

    • 9:00 – 9:45 : Talk

      Title
      Abstract
    • 9:45 – 10:30 : Yingtong Hou – IECL

      Butcher series: from ordinary differential equations to Rough Path Theory and Regularity Structures
      In this talk, I will give a gentle introduction to Butcher series (B-series), Rough Path Theory, Regularity Structures, and their underlying Hopf algebras. Rough Path Theory and Regularity Structures provide pathwise frameworks for solving rough differential equations (RDEs) and singular stochastic partial differential equations (SPDEs), respectively. We will see that all these pathwise solution ansatz are obtained from iterating Taylor expansions. Therefore, Rough Path Theory and Regularity Structures can be viewed as generalisations of B-series designed for solving ordinary differential equations (ODEs). I will present the derivation of B-series-type solution ansatz for ODEs, RDEs, and SPDEs. Rooted trees and Hopf algebras appear naturally in encoding the expansions of solution ansatz. No prior background knowledge in rough analysis is required. Familiarity with Taylor expansions will be sufficient.
    • 10:30 – 11:00 : Break
    • 11:00 – 11:45 : Talk

      Title
      Abstract
    • 11:45 – 12:30 : Juan Mardomingo-Sanz – IECL

      Slow-fast limits of stochastic particle systems arising in telomere biology
      The ends of linear chromosomes, called telomeres, shorten at each cell replication, eventually driving the cells to a senescent state when they become too short. The enzyme telomerase, present in cancerous cells and some unicellular organisms, elongates the telomeres and allows cells to continue replicating. Recent experiments show that if this enzyme is inactivated some rare survivors (ALT), which elongate their telomeres without telomerase, will appear and will eventually invade the cultures.
      I will present a simple stochastic particle system which accounts for the emergence and invasion of these ALT cells under an appropriate scaling with different speeds for each cell type.
    • 12:30 – 14:00 : Lunch
    • 14:00 – 14:45 : Talk

      Title
      Abstract
    • 15:00 – 17:30 : Scavenger Hunt in the city (Luxembourg)
    • 19:00 : Social Dinner at Brasserie du Cercle (Luxembourg City)

Friday 22/05 – MSA 3.500 :

    • 9:00 – 9:45 : Gautier Schanzenbacher – IECL

      An Introduction to Hyperbolic Geometry: Surfaces, Geodesics, and Entropy
      For centuries, mathematicians tried to prove Euclid’s fifth axiom (the parallel postulate) using only the first four. In the 19th century, Gauss showed that replacing this axiom leads to a new, consistent geometry: non-Euclidean geometry. In particular, if we suppose that there are infinitely many lines parallel to a given line passing through a single point, we obtain Hyperbolic Geometry.
      In this talk, I will start from these foundations to define hyperbolic surfaces. We will then explore the world of curves, geodesics, and homotopy classes to understand the concept of entropy of the geodesic flow of a hyperbolic surface in the simplest way possible.
    • 9:45 – 10:30 : Talk

      Title
      Abstract
    • 10:30 – 11:00 : Break
    • 11:00 – 11:45 : Musbahu Idris – IECL

      Algorithmic Aspects of Newman Polynomials and Their Divisors
      A Newman polynomial is a polynomial with coefficients in ${0,1}$ and constant term $1$. We investigate which integer-coefficient polynomials divide a Newman polynomial, focusing on those with small Mahler measure. Using mixed-integer linear programming, we determine the divisibility status of all $8,438$ known polynomials with Mahler measure less than $1.3$. We further exhibit new polynomials that divide no Newman polynomial, improving the best known upper bound on a conjectural universal constant $\sigma$ to approximately $1.419$.
    • 11:45 – 12:30 : Talk

      Title
      Abstract
    • 12:30 – 14:00 : Lunch