14 citations · 17 across the 10 of their papers we have counts for
15 papers · 1 filter
A counterexample to Purdy's inequality for hyperplane arrangements in projective three-space
Mateusz Michałek, Piotr Pokora
We record an explicit counterexample to a refined form of Purdy's inequality for essential hyperplane arrangements in projective three-space. Let be an arrangement of…
Sullivant-Talaska ideal of the cyclic Gaussian Graphical Model
Austin Conner, Kangjin Han, Mateusz Michałek
In this paper, we settle a conjecture due to Sturmfels and Uhler concerning generation of the prime ideal of the variety associated to the Gaussian graphical model of any cycle gra…
Khovanskii bases for semimixed systems of polynomial equations -- a case of approximating stationary nonlinear Newtonian dynamics
Viktoriia Borovik, Paul Breiding, Javier del Pino +2
We provide an approach to counting roots of polynomial systems, where each polynomial is a general linear combination of prescribed, fixed polynomials. Our tools rely on the theory…
Enumerative geometry meets statistics, combinatorics and topology
Mateusz Michałek
We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on di…
Geometry of the Gaussian graphical model of the cycle
Rodica Andreea Dinu, Mateusz Michałek, Martin Vodička
We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods bas…
Applications of intersection theory: from maximum likelihood to chromatic polynomials
Rodica Andreea Dinu, Mateusz Michałek, Tim Seynnaeve
Recently, we have witnessed tremendous applications of algebraic intersection theory to branches of mathematics, that previously seemed very distant. In this article we review some…