Sergey Avvakumov

activity

20242026

collaborators

4 papers

math.CO2026

The affine Tverberg theorem revisited

Sergey Avvakumov, Roman Karasev

We prove the Bárány--Kalai--Tverberg conjecture extending the affine version of Tverberg's theorem to simplicial balls and polytopes other than the simplex: For any affine map $ϕ:…

math.CO2025

Tensor rank of the determinant and periodic triangulations of $R^{n}$

Sergey Avvakumov, Roman Karasev

We prove that in any $Z^{n}$ -periodic triangulation of $R^{n}$ the number of $Z^{n}$ -orbits of $n$ -dimensional simplices is at least the tensor rank of the $n$ …

math.CO2025

Cubulating the sphere with many facets

Sergey Avvakumov, Alfredo Hubard

For each $d \geq 3$ we construct cube complexes homeomorphic to the $d$ -sphere with $n$ vertices in which the number of facets (assuming $d$ constant) is $Ω (n^{5/4})$ . This disprove…

math.DG2024

Small separators, upper bounds for $l^{\infty}$ -widths, and systolic geometry

Sergey Avvakumov, Alexander Nabutovsky

We investigate the dependence on the dimension in the inequalities that relate the Euclidean volume of a closed submanifold $M^{n} \subset R^{N}$ with its $l^{\infty}$ -width $W^{…

The affine Tverberg theorem revisited

Tensor rank of the determinant and periodic triangulations of Rn

Cubulating the sphere with many facets

Small separators, upper bounds for l∞-widths, and systolic geometry

Tensor rank of the determinant and periodic triangulations of $R^{n}$

Small separators, upper bounds for $l^{\infty}$ -widths, and systolic geometry