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Personal Profile of Jason Morton

Jason Morton
Department of Mathematics
  1. Summer Graduate School Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas

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    Jul 07, 2008
    Monday
    10:15 AM - 11:15 AM
      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
    Jason Morton (Pennsylvania State University)
    Jul 08, 2008
    Tuesday
    09:00 AM - 10:00 AM
      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
    Jason Morton (Pennsylvania State University)
    Jul 09, 2008
    Wednesday
    10:15 AM - 11:15 AM
      § 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.
    Jason Morton (Pennsylvania State University)
    Jul 10, 2008
    Thursday
    09:00 AM - 10:00 AM
      Toric varieties, toric ideals, moment map, exponential families.
    Jason Morton (Pennsylvania State University)
    Jul 11, 2008
    Friday
    09:00 AM - 10:00 AM
      finish Ch 4 (Littlewood-Richardson rule and other handy formulas, more decompositions of spaces of tensors)
    Jason Morton (Pennsylvania State University)
    Jul 14, 2008
    Monday
    09:00 AM - 10:00 AM
      § 5.4, 5.5 Equations II: inheritance, and prolongation
    Jason Morton (Pennsylvania State University)
    Jul 15, 2008
    Tuesday
    10:15 AM - 11:15 AM
      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.
    Jason Morton (Pennsylvania State University)