4 papers
Polynomial valuations on plane polygons
Askold Khovanskii, Valentina Kiritchenko, Vladlen Timorin
Scissors congruence problems involving translations have prompted the study of translation invariant simple valuations. We review this classical theory from a naive and consistent…
A necessary condition for solvability by radicals
Askold Khovanskii
This note was prepared as a handout for the MAT401 course ``Polynomial equations and fields", taught at the University of Toronto in Spring 2026. It presents a proof of a necessary…
Galois theory for finite fields
Askold Khovanskii
This note presents Galois theory for finite fields. It was written as a handout for the MAT401 course ``Polynomial equations and fields'' taught at the University of Toronto in Spr…
Valuations on polyhedra and topological arrangements
Askold Khovanskii, Valentina Kiritchenko, Vladlen Timorin
We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously…