62 citations · 222 across the 34 of their papers we have counts for
5 papers · 1 filter
Geometric complexity theory and matrix powering
Fulvio Gesmundo, Christian Ikenmeyer, Greta Panova
Valiant's famous determinant versus permanent problem is the flagship problem in algebraic complexity theory. Mulmuley and Sohoni (Siam J Comput 2001, 2008) introduced geometric co…
The geometry of rank decompositions of matrix multiplication I: 2x2 matrices
Luca Chiantini, Christian Ikenmeyer, J. M. Landsberg +1
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors,…
On the complexity of the permanent in various computational models
Christian Ikenmeyer, J. M. Landsberg
We answer a question in [Landsberg, Ressayre, 2015], showing the regular determinantal complexity of the determinant det_m is O(m^3). We answer questions in, and generalize results…
On the relative power of reduction notions in arithmetic circuit complexity
Christian Ikenmeyer, Stefan Mengel
We show that the two main reduction notions in arithmetic circuit complexity, p-projections and c-reductions, differ in power. We do so by showing unconditionally that there are po…
No occurrence obstructions in geometric complexity theory
Peter Bürgisser, Christian Ikenmeyer, Greta Panova
The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VP_{ws} and VNP. Mulmuley and Soh…