G. Ivanov

activity

20242026

collaborators

Showing 2024Show all

6 papers · 1 filter

math.MG2024

The John inclusion for log-concave functions

G. Ivanov

John's inclusion states that a convex body in $R^{d}$ can be covered by the $d$ -dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-con…

math.CO2024

Helly numbers for Quantitative Helly-type results

G. Ivanov, M. Naszodi

We obtain three Helly-type results. First, we establish a Quantitative Colorful Helly-type theorem with the optimal Helly number $2d$ concerning the diameter of the intersection…

math.FA2024

No-dimensional Helly's theorem in uniformly convex Banach spaces

G. Ivanov

We study the ``no-dimensional'' analogue of Helly's theorem in Banach spaces. Specifically, we obtain the following no-dimensional Helly-type results for uniformly convex Banach sp…

math.MG2024

Tight colorful no-dimensional Tverberg theorem

Polina Barabanshchikova, Grigory Ivanov, Alexander Polyanskii

We study colorful no-dimensional Tverberg-type problems and obtain several optimal results. A colorful no-dimensional Tverberg-type theorem provides a bound on a radius $R$ such th…

math.CO2024

Colorful positive bases decomposition and Helly-type results for cones

Grigory Ivanov

We prove the following colorful Helly-type result: Fix $k \in [d - 1]$ . Assume $A_{1}, \dots, A_{d + (d - k) + 1}$ are finite sets (colors) of nonzero vectors in $R^{d}$ .…

math.MG2024

Quantitative Steinitz theorem and polarity

Grigory Ivanov

The classical Steinitz theorem asserts that if the origin lies within the interior of the convex hull of a set $S \subset R^{d}$ , then there are at most $2 d$ points in $S$ w…