Joseph M. Landsberg

TL;DR: In this article, a new explicit description of each of these irreducible components is provided, which is a parametrization of each component, and one can explicitly construct any pencil in each component.

TL;DR: In this paper, the rigidity of submanifolds of projective spaces is studied, and the results of [16, 20, 29, 18, 19, 10, 31] are surveyed.

Abstract: This is an expanded and updated version of a lecture series I gave at Seoul National University in September 1997. It is in some sense an update of the 1979 Griffiths and Harris paper with a similar title. I discuss: Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, When can a uniruled variety be smooth?, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, Systems of quadrics with tangential defects, Recognizing uniruled varieties, Recognizing intersections of quadrics, Recognizing homogeneous spaces, Complete intersections. This is a preliminary version, so please send me comments, corrections and questions.

TL;DR: In this article, the linear strand of the minimal free resolution of the ideal generated by k x k sub-permanents of an n x n generic matrix and by square-free monomials of degree k was computed.

TL;DR: In this article, the Deep Null-Space-Property (DNSP) was proposed to guarantee the stable recovery of the matrix factors in a deep convolutional network, which can be applied to many fast transforms such as FFT.