40 citations · 460 across the 64 of their papers we have counts for
8 papers · 1 filter
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…
Interlacing Ehrhart Polynomials of Reflexive Polytopes
Akihiro Higashitani, Mario Kummer, Mateusz Michałek
It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann ζ function. The construction was generalized by Matsui et al.…
Flexible affine cones and flexible coverings
Matheusz Michałek, Alexander Perepechko, Hendrik Süß
We provide a new criterion for flexibility of cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant va…
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^…
Finite phylogenetic complexity and combinatorics of tables
Mateusz Michałek, Emanuele Ventura
We prove that the phylogenetic complexity -- an invariant introduced by Sturmfels and Sullivant -- of any finite abelian group is finite.
The poset of rational cones
Joseph Gubeladze, Mateusz Michałek
We introduce a natural partial order on the set Cones(d) of rational cones in R^d. The poset NPol(d-1) of normal polytopes in R^{d-1} embeds into Cones(d) via the homogenization ma…
On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry
J. M. Landsberg, Mateusz Michałek
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors w…
Real Rank Geometry of Ternary Forms
Mateusz Michałek, Hyunsuk Moon, Bernd Sturmfels +1
We study real ternary forms whose real rank equals the generic complex rank, and we characterize the semialgebraic set of sums of powers representations with that rank. Complete re…