2025/2026 Seminars

Abstract: A model for the modes of vibration of an idealized drumhead is given by Dirichlet eigenfunctions. To each of them it is associated a positive number called eigenvalue. This quantity is related to the frequency of the sound produced by the drum when the drumhead vibrates in the corresponding mode. 

In this seminar we introduce a new type of eigenfunctions that satisfy an orthogonality constraint with respect to a given function. Finally we treat some shape optimization problems relative to the corresponding eigenvalues.

Based on a joint work with D. Zucco. 

Abstract: Should (gender) diversity and inclusivity in maths still be discussed nowadays? 

Based on a survey made in 2025 among maths students, PhD students and postdocs throughout the world, the first part of the talk will provide powerful insights on various topics (gender quotas, work-life balance, role models, menstruations and stereotypes), leading to a second part where we will have an interactive discussion together with the audience.

Abstract: Class groups of fields give important information about unique factorisation in their ring of integers, in particular they played a major role in the study of Fermat's Last Theorem. In this talk we will first introduce what class groups are and then, following the last 200 years of mathematical progress in the topic, introduce Ribet's Method, a powerful technique combining modular forms and Galois representations, used to study class groups. We will end with a new cohomological approach to this method. 

Abstract: A derangement is a permutation with no fixed points. By a classical result of Jordan, any nontrivial finite transitive permutation group contains such elements. This fact has far-reaching applications and raises natural questions about the abundance and orders of derangements, which have been widely studied in recent years. In this talk, I will survey some of these problems and results, and I will discuss how combinatorial tools can be used to obtain simple formulas for the proportion of derangements in certain natural subgroups of the finite affine general linear group.  

Abstract: We consider a model for an electrically charged liquid drop laying on a solid surface. The surface tension of the droplet is represented by the classical De Giorgi perimeter with a capillarity modification whereas the electric charge is modeled by the Riesz energy. We study the resulting functional under convexity constraint in dimension 2, focusing on existence and regularity of minimizers. In the end we show the validity of Young's law, describing the contact angle between the droplet and the supporting surface.  

Abstract: We will study the evolution of the motion of a fluid surrounded by vacuum. This evolution is described by the two-dimensional incompressible Navier–Stokes equations.

The regularity of the motion depends both on the smoothness of the initial velocity field of the fluid and on the geometry of the region Ω initially occupied by it. In particular, we are interested in the case where Ω is a Lipschitz domain. We will show that, under a mild regularity assumption on the initial velocity field (belonging to a critical Besov space), the evolved region Ω_t remains Lipschitz.

The proof relies on Dynamic Interpolation, a time-dependent version of the classical Real Interpolation method for Banach spaces. To introduce this technique and the role of Besov spaces, we will first discuss the heat equation as a simpler toy model for the Navier–Stokes system.