6 citations · 20 across the 10 of their papers we have counts for
18 papers
Quantitative Steinitz theorem: A spherical version
Grigory Ivanov, Márton Naszódi
Steinitz's theorem states that if the origin belongs to the interior of the convex hull of a set , then there are at most points of whos…
Functional John and Löwner conditions for pairs of log-concave functions
Grigory Ivanov, Márton Naszódi
John's fundamental theorem characterizing the largest volume ellipsoid contained in a convex body in has seen several generalizations and extensions. One directi…
Quantitative Steinitz Theorem: A polynomial bound
Grigory Ivanov, Márton Naszódi
The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set , then there are at most points of who…
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…
Geometric representation of classes of concave functions and duality
Grigory Ivanov, Elisabeth M. Werner
Using a natural representation of a -concave function on as a convex set in we derive a simple formula for the integral of its -polar. Th…
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…
Functional John Ellipsoids
Grigory Ivanov, Márton Naszódi
We introduce a new way of representing logarithmically concave functions on . It allows us to extend the notion of the largest volume ellipsoid contained in a conve…
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 …
Orthodiagonal anti-involutive Kokotsakis polyhedra
Ivan Erofeev, Grigory Ivanov
We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flex…
On the volume of projections of the cross-polytope
G. Ivanov
We study properties of the volume of projections of the -dimensional cross-polytope $\crosp^n = \{ x \in \R^n \mid |x_1| + \dots + |x_n| \leqslant 1\}.$ We prove that the projec…
Tight frames and related geometric problems
Grigory Ivanov
We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of onto We show that a set of ve…
On the volume of the John-Löwner ellipsoid
Grigory Ivanov
We find an optimal upper bound on the volume of the John ellipsoid of a -dimensional section of the -dimensional cube, and an optimal lower bound on the volume of the Löwner…
Hypomonotonicity of the normal cone and proximal smoothness
Grigory Ivanov
In this paper we study the properties of the normal cone to the proximally smooth set. We give the complete characterization of the proximally smooth set through the monotony prope…
Modulus of supporting convexity and supporting smoothness
Grigory Ivanov
We introduce the moduli of the supporting convexity and the supporting smoothness of a Banach space, which characterize the deviation of the unit sphere from an arbitrary supportin…
Convex hull deviation and contractibility
Grigory Ivanov
We study the Hausdorff distance between a set and its convex hull. Let be a Banach space, define the CHD-module of space as the supremum of this distance for all subset of…