6 papers
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…
Probabilistic intersection theory in Riemannian homogeneous spaces
Paul Breiding, Peter Bürgisser, Antonio Lerario +1
Let be a Riemannian homogeneous space, where is a compact Lie group with closed subgroup . Classical intersection theory states that the de Rham cohomology ring of $…
The Grassmann distance complexity
Antonio Lerario, Andrea Rosana
Motivated by the concept of Euclidean Distance Degree, which measures the complexity of finding the nearest point to an algebraic set in Euclidean space, we introduce the notion of…
What is... Random Algebraic Geometry?
Antonio Lerario
We survey some ideas from the subject of Random Algebraic Geometry, a field that introduces a probabilistic perspective on classical topics in real algebraic geometry. This offers…