2025/2026 Seminars

Abstract: A fundamental concept in geometry is the volume, which quantifies the extension of an object. The first formulas we learn at school are those to compute how big rectangles and triangles are. As mathematicians we have more sophisticated objects, like Riemannian manifolds, whose metric structure allows to compute volumes (and many other things). What can we do if dealing just with a topological manifold, which can be stretched and deformed while remaining exactly the same topologically, and volumes are meaningless? This premise is an excuse to give a basic introduction to the "minimal" and the "simplicial" volume, two invariants introduced by Gromov (80s). 

Abstract: In 1050, Milnor introduced a definition of Total Curvature for rectifiable curves in R^n. In 2023, Mucci and Saracco proposed a definition of p-curvature for any exponent p >= 1, showing that a rectifiable curve parametrized by arc length belongs to the Sobolev space W^{2,p} if and only if its p-curvature is finite. Moreover, in this case, the p-curvature equals the integral on the curve of the p-th power of the norm of its curvature. In this seminar, I will explain how the concept of p-curvature can be extended to rectifiable curves in the sphere and how analogous results can be obtained in this setting. This is joint work D. Mucci and A. Saracco

Abstract: General Relativity, dating back to Einstein's 1915 proposal, is the most accurate and succesful classical theory of gravitation in modern physics. In this talk, we present its mathematical framework, starting from the interpretation of gravity in terms of the curvature of a 4D Lorentzian manifold and up to the PDE theory behind the hyperbolic quasilinear system of the Einstein equations. In the final part of the talk, we will discuss black hole spacetimes and some recent progress on the celebrated cosmic censorship conjectures

Abstract: We will present a nonlinear exchange dynamics for Ising spin systems with arbitrary interactions, described by a quadratic Boltzmann-type equation that preserves the mean magnetization. In particular, we will discuss convergence to the Ising equilibrium and, for weak interactions, exponential relaxation in relative entropy, proved using a kinetic approach inspired by Kac's program.

Based on joint work with Pietro Caputo.

Abstract: How much of  an infinite group can be recovered from its finite quotients? Often, not much, but when restricted to certain classes of groups they become surpisingly effective at describing the group structure. After introducing free products and free factors, I'll explain how such decompositions leave traces in finite quotients and discuss why turning those traces into detection theorems is subtle, highlighting examples, recent progress and open problems.

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.