Complexity of matrix multiplication, an overview of Ch. 2 including tensors, rank of tensors, and wiring diagrams. Date: July 07, 2008 29 views • about 10 years ago

The Alexander-Hirschowitz theorem Date: July 18, 2008 17 views • about 10 years ago

What do the words "ACM", "Gorenstein", and " rational singularites" mean and why are these properties useful? Date: July 16, 2008 11 views • about 10 years ago

Notions of tensor ranks: rank, border rank, multilinear rank, nonnegative rank Date: July 08, 2008 7 views • about 10 years ago

§ 4.3,4,5 - Representations of the symmetric group, Young diagrams, Young symmetrizers and wiring diagrams. Using these tools to decompose V^{\otimes d} as a GL(V) module. Schur-Weyl Duality. Date: July 09, 2008 7 views • about 10 years ago

Algebraic varieties § 3.1, 3.2. Basic definitions from algebraic geometry: projective space, variety, ideal, Zariski topology. Segre, Veronese, and other examples of varieties. Graphical models and motivating examples in statistics and information t Date: July 07, 2008 7 views • about 10 years ago

Toric varieties, toric ideals, moment map, exponential families. Date: July 10, 2008 7 views • about 10 years ago

§ 3.3,4,5,6 Tangent spaces to varieties, joins, cones, secant varieties, their dimension, Terracini's lemma. Date: July 08, 2008 7 views • about 10 years ago

Tensor approximations Date: July 07, 2008 6 views • about 10 years ago

Non-commutative harmonic analysis in machine learning Date: July 14, 2008 5 views • about 10 years ago

§ 6.1,6.2,6.6,6.7 The Alexander-Hirshowitz theorem and dimensions of secant varieties of Segre varieties Date: July 15, 2008 5 views • about 10 years ago

Uniqueness of tensor decomposition, direct sum conjecture Date: July 14, 2008 5 views • about 10 years ago

Introduction to the study of G-varieties via desingularizations by homogeneous vector bundles Date: July 17, 2008 5 views • about 10 years ago

§ 4.6,7,8 Highest weight vectors, bases of highest weight space. Ideals of Segre, Veronese varieties and homogeneous varieties in general, decomposing S^d(A_1\otimes \cdots \otimes A_n), characters. Date: July 10, 2008 4 views • about 10 years ago

Hyperdeterminants and optimal approximability Date: July 11, 2008 3 views • about 10 years ago

Induction for the rank of tensors Date: July 18, 2008 3 views • about 10 years ago

Phylogenetic algebraic geometry Date: July 10, 2008 3 views • about 10 years ago

finish Ch 4 (Littlewood-Richardson rule and other handy formulas, more decompositions of spaces of tensors) Date: July 11, 2008 3 views • about 10 years ago

(d) the invertible case: Independent Component Analysis - optimization criteria and some numerical algorithms Date: July 17, 2008 3 views • about 10 years ago

Student Lecture Date: July 18, 2008 2 views • about 10 years ago