Il ciclo di seminari Incontri Matematici “Federigo Enriques” prevede quattro incontri annuali. Il calendario per il 2026 è attualmente in fase di definizione e ogni aggiornamento sarà pubblicato su questa pagina non appena disponibile.
IHÉS, Paris
19/05/2026 – 16:30
Aula C03, Via Mangiagalli 25, Milano
Titolo: Some modern aspects of Weil’s “Rosetta Stone”
Abstract. There is a classical analogy between number fields and Riemann surfaces, which has been present and useful since the beginning of these theories. André Weil was enchanted with this analogy: he wrote about it in a letter to his sister, where he described a third theory mediating between number fields and Riemann surfaces, and likened this trinity to the Rosetta Stone. In recent years, this analogy has deepened and transformed in remarkable ways. I will describe the classical story and some more modern aspects.
Università Bocconi
18/03/2026 – 16:30
Aula 301, Via Celoria 20, Milano
Titolo: Structure of the manifold of accessible fixed points in asymmetric Neural Networks and its consequences for learning: A Gradient-Free Approach to machine learning
Abstract. We study asymmetric recurrent neural networks as high-dimensional dynamical systems and identify a regime in which the dynamics gives rise to an exponentially large set of stable fixed points forming a connected and dynamically accessible manifold. Rather than being isolated solutions scattered throughout configuration space, these fixed points concentrate in a dense region characterized by positive local entropy. Using tools from high-dimensional probability and statistical mechanics, we analyze the geometry of this fixed-point set and show that, beyond a critical coupling threshold, a structural transition occurs: isolated solutions give way to a connected cluster that can be reached by simple iterative dynamics. This transition is closely related to phenomena underlying the Overlap Gap Property and the onset of algorithmic hardness in random constraint satisfaction problems. While typical fixed points remain isolated and inaccessible to local algorithms, subdominant high-density regions become dynamically reachable. We derive explicit thresholds for the emergence of this accessible cluster and provide analytic bounds ensuring convergence of the intrinsic dynamics. Building on this geometric structure, we introduce a learning mechanism that stabilizes single task-relevant configurations via strictly local updates, without resorting to gradient descent or global loss minimization. Numerical experiments show that this stabilization principle yields performance comparable to standard multilayer perceptrons with matched parameter counts on benchmark tasks.