9 papers
Erdős--Ko--Rado and Hilton--Milner theorems for two-forms
Grigory Ivanov, Seyda Köse
In this short note we show that both generalizations of celebrated Erdős--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial…
A Quantitative Helly-type Theorem: Containment in a Homothet
Grigory Ivanov, Márton Naszódi
We introduce a new variant of quantitative Helly-type theorems: the minimal \emph{"homothetic distance"} of the intersection of a family of convex sets to the intersection of a sub…
Rectifiable curves in proximally smooth sets
Grigory Ivanov, Mariana Lopushanski
We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space…
Functional Löwner Ellipsoids
Grigory Ivanov, Igor Tsiutsiurupa
We extend the notion of the smallest volume ellipsoid containing a convex body in~ to the setting of logarithmically concave functions. We consider a vast class of…
On the volume of sections of the cube
Grigory Ivanov, Igor Tsiutsiurupa
We study the properties of the maximal volume -dimensional sections of the -dimensional cube . We obtain a first order necessary condition for a -dimensional sub…
Approximation of the average of some random matrices
Grigory Ivanov, Márton Naszódi, Alexandr Polyanskii
Rudelson's theorem states that if for a set of unit vectors and positive weights , we have that is the identity operator on …