From the 1 of 10 linked papers with an AI index.
10 papers
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
The paper establishes dimension bounds for abnormal and Goh‑abnormal sets in rank‑2 polarized metabelian Lie groups, proving that the endpoint map satisfies the Sard property and t…
Sard properties for polynomial maps in infinite dimension
Antonio Lerario, Luca Rizzi, Daniele Tiberio
Sard's theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional B…
The Denario project: Deep knowledge AI agents for scientific discovery
Francisco Villaescusa-Navarro, Boris Bolliet, Pablo Villanueva-Domingo +33
We present Denario, an AI multi-agent system designed to serve as a scientific research assistant. Denario can perform many different tasks, such as generating ideas, checking the…
Thom-Milnor bounds for smooth manifolds
Saugata Basu, Antonio Lerario, Matteo Testa
We prove a smooth analogue of the classical Thom-Milnor bound, showing that the Betti numbers of the zero set of a smooth map on a compact Riemannian manifold can be controlled by…
Testing the variety hypothesis
A. Lerario, P. Roos Hoefgeest, M. Scolamiero +1
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of g…
-invariant Gaussian measures on the space of -adic polynomials
Yassine EL Maazouz, Antonio Lerario
We prove that if there is a unique gaussian distribution (in the sense of Evans) on the space which is invariant under the action of $\…