18 citations · 34 across the 20 of their papers we have counts for
20 papers
A sub-Riemannian endpoint map with no regular values
Antonio Lerario, Luca Rizzi, Daniele Tiberio
We construct an endpoint map with no regular values, disproving the sub-Riemannian Sard conjecture. Remarkably, in our construction the minimizing Sard property remains valid.
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
We provide sharp bounds on the dimension of the abnormal set for rank polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such group…
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…
Quantitative approximate definable choices
Antonio Lerario, Luca Rizzi, Daniele Tiberio
In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist b…
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 probabilistic method in real singularity theory
Antonio Lerario, Michele Stecconi
We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e. with total Betti number of the maximal possible orde…
How regularization affects the geometry of loss functions
Nathaniel Bottman, Y. Cooper, Antonio Lerario
What neural networks learn depends fundamentally on the geometry of the underlying loss function. We study how different regularizers affect the geometry of this function. One of t…
A proof of the Hamiltonian Thom Isotopy Lemma
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
In this note we present a complete proof of the fact that all the submanifolds of a one parameter family of compact symplectic submanifolds inside a compact symplectic manifold are…
What is the probability that a random symmetric tensor is close to rank-one?
Alberto Cazzaniga, Antonio Lerario, Andrea Rosana
We address the general problem of estimating the probability that a real symmetric tensor is close to rank-one tensors. Using Weyl's tube formula, we turn this question into a diff…
Optimal transport between algebraic hypersurfaces
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing t…
-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 $\…
Symplectic Instability of Bézout's Theorem
Michele Ancona, Antonio Lerario
We investigate the failure of Bézout's Theorem for two symplectic surfaces in (and more generally on an algebraic surface), by proving that every plane alg…
Maximal and Typical Topology of Real Polynomial Singularities
Antonio Lerario, Michele Stecconi
Given a polynomial map with components of degree , we investigate the structure of the semialgebraic set consisting of those points wher…
Geodesics and admissible-path spaces in Carnot Groups
A. A. Agrachev, A. Gentile, A. Lerario
We study the topology of admissible-loop spaces on a step-two Carnot group G. We use a Morse-Bott theory argument to study the structure and the number of geodesics on G connecting…
Systems of Quadratic Inequalities
Andrei Agrachev, Antonio Lerario
We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the…