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pro vyhledávání: '"Lerario, A."'
Motivated by the Sard conjecture in sub-Riemannian geometry, and more specifically on Carnot groups, we consider the set of maps defined on a Hilbert space $H$: \[\mathscr{P}_{d}^m(H)=\bigg\{f:H\to \mathbb{R}^m\,\bigg|\, \forall\, E\subset H, \,\dim(
Externí odkaz:
http://arxiv.org/abs/2407.02296
Given two closed subsets $X, Y$ in $\mathbb{R}^n$, we construct a version of Morse Theory for $\mathrm{dist}_Y|_X \colon X \to \mathbb{R}$, the restriction to $X$ of the Euclidean distance function from $Y$. We use the notion of critical points of Li
Externí odkaz:
http://arxiv.org/abs/2402.08639
Autor:
Lerario, Antonio, Stecconi, Michele
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 order. We show how similar ideas can be used to produce real algebraic pro
Externí odkaz:
http://arxiv.org/abs/2308.00050
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 the most basic geometric properties of a smooth function is whether it
Externí odkaz:
http://arxiv.org/abs/2307.15744
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 Hamiltonian isotopic.
Comment: arXiv admin note: substantial tex
Comment: arXiv admin note: substantial tex
Externí odkaz:
http://arxiv.org/abs/2307.06826
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 differential geometric one involving the study of metric invariants of the
Externí odkaz:
http://arxiv.org/abs/2301.05502
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 the optimal transport problem between complex algebraic projective hype
Externí odkaz:
http://arxiv.org/abs/2212.10274
Autor:
Maazouz, Yassine EL, Lerario, Antonio
We prove that if $p>d$ there is a unique gaussian distribution (in the sense of Evans) on the space $\mathbb{Q}_p[x_1, \ldots, x_n]_{(d)}$ which is invariant under the action of $\mathrm{GL}(n, \mathbb{Z}_p)$ by change of variables. This gives the no
Externí odkaz:
http://arxiv.org/abs/2209.13634
Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the Cosmic Microwave Background radiation. These objects can be viewed as
Externí odkaz:
http://arxiv.org/abs/2207.08413
Autor:
Lerario, Antonio, Tripaldi, Francesca
The aim of this paper is to give a thorough insight into the relationship between the Rumin complex on Carnot groups and the spectral sequence obtained from the filtration on forms by homogeneous weights that computes the de Rham cohomology of the un
Externí odkaz:
http://arxiv.org/abs/2206.07135