Emanuele Salato, Politecnico di Torino

Emanuele Salato | Politecnico di Torino 

When: February 6th, 2026 at 4 pm

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract:   The movement of the membrane that produces a sound emitted by an ideal drum can be decomposed in a countable quantity of vibrations. The profiles of these vibrations can be described by means of the Dirichlet eigenfunctions corresponding to the shape of the membrane. To each eigenfunction it is associated a positive number called eigenvalue. The square root of this value represents, up to a multiplicative constant depending on physical parameters, the frequency of the sound produced by the vibration described by the corresponding eigenfunction.

In this seminar, after a revision of the classical theory, we introduce a new type of eigenfunctions that satisfy orthogonality constraints with respect to a given family of functions. Finally, time permitting, we treat some shape optimization problems regarding the corresponding eigenvalues. This talk contains a part of the results achieved working with Dorin Bucur and Davide Zucco.

Giorgia Petracci, Università degli studi dell'Insubria

When: February 17th, 2026 at 5 pm

Where: Seminario 2 (Dip. Mat. UNIBO)

Abstract:  A $\text{G}_2$-structure on a 7-dimensional manifold M is a reduction of its frame bundle from $\text{GL}(7,\mathbb{R})$ to the exceptional Lie group $\text{G}_2\subset \text{SO}(7)$. Such a reduction is equivalent to the existence of a certain positive $3$-form $\phi$. This form defines a Riemannian metric $g_{\phi}$ and an orientation $\text{vol}_{\phi}$ on M, hence a Hodge operator $*_{\phi}$. When $\phi$ is parallel with respect to the Levi-Civita connection of $g_\phi$, the identity component of its holonomy group is contained in $\text{G}_2$; in fact, $\text{G}_2$ is one of the two exceptional Lie groups appearing in the celebrated Berger's classification of Riemannian holonomy groups. A $\text{G}_2$-structure is called {\it closed} if $d\phi=0$, and {\it coclosed} if $d*_\phi\phi=0$. We study left-invariant $\text{G}_2$-structures on nilmanifolds, which are compact quotients of connected, simply connected, nilpotent Lie groups by a lattice.  

Francesca De Giovanni, University of Naples Federico II

https://www.researchgate.net/profile/Francesca-De-Giovanni-2

When: February 24th, 2026 at 5 pm

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract: The optimization of eigenvalues of elliptic operators with respect to the geometry of the domain is a central topic in spectral geometry and shape optimization. In many classical settings, and in particular among domains with fixed volume, the ball arises as the optimal shape, either minimizing or maximizing the first eigenvalue.

In this talk, we focus on the first eigenvalue of the p-Laplacian under several types of boundary conditions and we investigate its behavior from both an optimization and an asymptotic point of view. For finite values of p, we discuss the validity of extremal properties, with special attention to Robin boundary conditions. We then analyze the behavior as p→+∞, showing that, in the case of a negative Robin parameter, the limit of the eigenvalues becomes independent of the geometry of the domain. Despite this apparent loss of geometric sensitivity, the ball continues to play an optimal role, answering in this particular case a long-standing conjecture.

Luca Melzi, Imperial College London

https://profiles.imperial.ac.uk/l.melzi24

When: May 12th, 2026 at 3:30 pm

Where: Seminario 1 (Dip. Mat. UNIBO)

Abstract: TBA