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By J. M. Landsberg.

Verified locator: Author prepublication manuscript, front matter copyright 2016; sections 1.1, 2.1, 4.7–4.8: bilinear complexity, tensor rank and border rank.

J. M. Landsberg works in algebraic geometry, differential geometry and their connections to computational complexity theory. His author page uses the name Joseph (JM) Landsberg and describes research on geometric questions arising from theoretical computer science.^[ref]

A central connection is to encode a bilinear map, such as matrix multiplication, by a tensor. Decomposing that tensor into pure tensors expresses a bilinear algorithm using scalar multiplications; tensor rank and border rank then distinguish exact decompositions from limiting ones. His work and books develop the geometry of these problems. His supplementary algebraic geometry notes introduce joins and secant varieties, which organize sums of points geometrically.^[ref] His Texas A&M profile lists algebraic and differential geometry among his research interests.^[ref]