8 citations · 22 across the 4 of their papers we have counts for
4 papers
The Algebraic Degree of Coupled Oscillators
Paul Breiding, Mateusz Michałek, Leonid Monin +1
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic comple…
Spaces of Sums of Powers and Real Rank Boundaries
Mateusz Michałek, Hyunsuk Moon
We investigate properties of Waring decompositions of real homogeneous forms. We study the moduli of real decompositions, so-called Space of Sums of Powers, naturally included in t…
A lower bound for the border rank of matrix multiplication
J. M. Landsberg, Mateusz Michałek
Let M_n denote the matrix multiplication tensor for nxn matrices. We use the border substitution method combined with Koszul flattenings to prove the border rank lower bound of 2n^…
Derived category of toric varieties with Picard number three
Arijit Dey, Michal Lason, Mateusz Michalek
We construct a full, strongly exceptional collection of line bundles on the variety X that is the blow up of the projectivization of the vector bundle O_{P^{n-1}}\oplus O_{P^{n-1}}…