44 citations · 138 across the 32 of their papers we have counts for
18 papers · 1 filter
Nonarchimedean integral geometry
Peter Bürgisser, Avinash Kulkarni, Antonio Lerario
Let be a nonarchimedean local field of characteristic zero with valuation ring , for instance, and . We prove a general integral geometric f…
Hausdorff approximations and volume of tubes of singular algebraic sets
Saugata Basu, Antonio Lerario
We prove bounds for the volume of neighborhoods of algebraic sets, in the euclidean space or the sphere, in terms of the degree of the defining polynomials, the number of variables…
Probabilistic enumerative geometry over -adic numbers: linear spaces on complete intersections
Rida Ait El Manssour, Antonio Lerario
We compute the expectation of the number of linear spaces on a random complete intersection in -adic projective space. Here "random" means that the coefficients of the polynomia…
Probabilistic Schubert Calculus: asymptotics
Antonio Lerario, Léo Mathis
In the recent paper [arXiv:1612.06893] P. Bürgisser and A. Lerario introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by t…
Betti Numbers of Random Hypersurface Arrangements
Saugata Basu, Antonio Lerario, Abhiram Natarajan
We study the expected behavior of the Betti numbers of arrangements of the zeros of random (distributed according to the Kostlan distribution) polynomials in $\mathbb{R}\mathrm{P}^…
Quantitative singularity theory for random polynomials
Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Motivated by Hilbert's 16th problem we discuss the probabilities of topological features of a system of random homogeneous polynomials. The distribution for the polynomials is the…