Roman N. Karasev

A Simpler Proof of the Boros---Füredi---Bárány---Pach---Gromov Theorem

A short and almost elementary proof of the Boros–Füredi–Bárány–Pach–Gromov theorem on the multiplicity of covering by simplices in ℝd is given.

Convex equipartitions: the spicy chicken theorem

We show that, for any prime power

Turán numbers for K s,t -free graphs: Topological obstructions and algebraic constructions

n

Dual theorems on central points and their generalizations

n and any convex body

Waist of the sphere for maps to manifolds

K

Notes About the Carathéodory Number

K (i.e., a compact convex set with interior) in