Sergey Avvakumov

collaborators

3 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…

The affine Tverberg theorem revisited

Tensor rank of the determinant and periodic triangulations of Rn

Cubulating the sphere with many facets

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