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 Creator(s):
 Jonathan Hauenstein
 Description:
StewartGough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic StewartGough platform is rigid with 40 assembly configurations (over the complex numbers) while exceptional StewartGough platforms have infinitely many assembly configurations and thus have selfmotion. We define a family of exceptional StewartGough platforms called Segredependent StewartGough platforms which aris…
 Date Created:
 20170117
 Record Visibility:
 Public

 Creator(s):
 Jonathan Hauenstein
 Description:
We define tensors, most of which correspond with cubic polynomials, which have the same exponent w as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor defined on an nxn matrix A by trace(A^3). The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent w.
 Date Created:
 20170107
 Record Visibility:
 Public

 Creator(s):
 Jonathan Hauenstein
 Description:
A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness sets via numerical elimination theory, we develop computational methods for computing ranks and border ranks of tensors along with decompositions. More generally, we present our approach using joins of any collection of irreducible and nondegenerate projecti…
 Date Created:
 20160831
 Record Visibility:
 Public