5 citations · 9 across the 4 of their papers we have counts for
4 papers
Partitioning Theorems for Sets of Semi-Pfaffian Sets, with Applications
Martin Lotz, Abhiram Natarajan, Nicolai Vorobjov
We generalize the seminal polynomial partitioning theorems of Guth and Katz to a set of semi-Pfaffian sets. Specifically, given a set of -dimensional s…
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}^…
Zeroes of polynomials on definable hypersurfaces: pathologies exist, but they are rare
Saugata Basu, Antonio Lerario, Abhiram Natarajan
Given a sequence of smooth and compact hypersurfaces in , we prove that (up to extracting subsequences) there exists a regular definab…
Computational Complexity of Certifying Restricted Isometry Property
Abhiram Natarajan, Yi Wu
Given a matrix with rows, a number , and , is -RIP (Restricted Isometry Property) if, for any vector , with at most non-zero…