Home / Videos / Semester(06-01-2008 - 07-31-2008)
Semester Workshops
06-01-2008 - 07-31-2008
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Joseph Landsberg:
Complexity of matrix multiplication, an overview of Ch. 2 including tensors, rank of tensors, and wiring diagrams.
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Jason Morton:
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
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Lek-Heng Lim:
Tensor approximations
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Jason Morton:
Finish Ch. 2: skew-symmetric tensors, equations for rank at most r linear mappings, border rank, decomposing V^{\ot 3}., G-modules, isotypic components. § 4.1,2 Representations, Schur's Lemma, G-modules and decomposing spaces of tensors
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Joseph Landsberg:
§ 3.3,4,5,6 Tangent spaces to varieties, joins, cones, secant varieties, their dimension, Terracini's lemma.
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Vin de Silva:
Notions of tensor ranks: rank, border rank, multilinear rank, nonnegative rank
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David Gross:
What is quantum information theory?
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Joseph Landsberg:
Finish Chap 3 - Terracini's lemma cont'd and applications to computing the dimension of secant varieties. The geometric definition of border rank, projective second fundamental form.
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Jason Morton:
§ 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.
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Lek-Heng Lim:
Conditioning, computations, applications
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Jason Morton:
Toric varieties, toric ideals, moment map, exponential families.
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Joseph Landsberg:
§ 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.
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Vin de Silva:
Constructibility of the set of tensors of a given rank
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Luis David Garcia Puente:
Phylogenetic algebraic geometry
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Jason Morton:
finish Ch 4 (Littlewood-Richardson rule and other handy formulas, more decompositions of spaces of tensors)
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Joseph Landsberg:
§ 5.1-5.3 Equations for secant varieties I: special Segre varieties, subspace varieties, flattenings
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Vin de Silva:
Hyperdeterminants and optimal approximability
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David Gross:
What are graph states?
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Jason Morton:
§ 5.4, 5.5 Equations II: inheritance, and prolongation
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Joseph Landsberg:
§ 5.6 Equations III: Strassen's equations and variants
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Vin de Silva:
Uniqueness of tensor decomposition, direct sum conjecture
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Risi Kondor:
Non-commutative harmonic analysis in machine learning
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Joseph Landsberg:
§ 6.1,6.2,6.6,6.7 The Alexander-Hirshowitz theorem and dimensions of secant varieties of Segre varieties
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Jason Morton:
Ch 7. An algorithm for explicitly writing down polynomials in a given submodule of the space of polynomials. Further combinatorics of Young tableaux. Working with tensors in factored vs. expanded form.
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Joseph Landsberg:
Ch 8: Rank vs border rank of tensors and symmetric tensors
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Luke Oeding:
The variety of principal minors of symmetric matrices
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Pierre Comon:
(a) general statements on linear mixtures of random variables, (b)cumulants, (c) tensors
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Jerzy Weyman:
What do the words "ACM", "Gorenstein", and " rational singularites" mean and why are these properties useful?
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Lek-Heng Lim:
Nonnegative hypermatrices, symmetric tensors
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Pierre Comon:
(d) the invertible case: Independent Component Analysis - optimization criteria and some numerical algorithms
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Jerzy Weyman:
Introduction to the study of G-varieties via desingularizations by homogeneous vector bundles
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Joseph Landsberg:
Ch 9: Spaces of tensors admitting normal forms
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Pierre Comon:
(e) the UDM case: some selected statistical blind identification approaches, all involving tensors. Local identifiability and numerical algorithms (including BIOME and FOOBI).
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Giorgio Ottaviani:
Induction for the rank of tensors
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Student Lecture
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Giorgio Ottaviani:
The Alexander-Hirschowitz theorem
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Ana Berrizbeitia, Alexander Moll, Laine Noble:
Structure of p-adic valuations of Stirling numbers
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Cindy Enrigue, Gerard Koffi, Loraine Torres Castro:
Landen Transformations with cot(3t)
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Richard Garcia Lebron, Aileen Nguyen, Ivan Ojeda, Bobby Wilson:
Analysis of the Dynamics of the Landen Transformations Using cot(4t)
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Ricela Feliciano-semidei, Marcos Ortiz, Jason Rosenberg, Kevin Wingfield:
Exploring a Rational Landen Transformation of Degree Eight
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Natasha Cayco Gajjic, Nathan Kallus, Jessica Stigile:
Numerical Intergration Techniques with Rational Landen Transformations
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