Browsing by Subject "algebraic geometry"

Now showing items 1-6 of 6

    • Applications of algebraic geometry to object/image recognition 
      Abbott, Kevin Toney (2009-06-02)
      In recent years, new approaches to the problem of Automated Target Recognition using techniques of shape theory and algebraic geometry have been explored. The power of this shape theoretic approach is that it allows one ...
    • Concise Tensors of Minimal Border Rank 
      Pal, Arpan (2023-08-02)
      We determine defining equations for the set of concise tensors of minimal border rank in C m⊗C m⊗C m when m = 5 and the set of concise minimal border rank 1∗-generic tensors when m = 5, 6. We solve the classical problem ...
    • Newton Polytopes and Numerical Algebraic Geometry 
      Brysiewicz, Taylor Christian (2020-04-17)
      We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface ...
    • On the structure tensor of sln 
      Bari, Kashif Karim (2021-04-23)
      The structure tensor of sln is the tensor arising from the Lie bracket bilinear operation on the set of traceless n by n complex matrices. This tensor is intimately related to the well studied matrix multiplication tensor. ...
    • Sparsity, Randomness and Convexity in Applied Algebraic Geometry 
      Ergur, Alperen Ali (2016-06-28)
      In this dissertation we study three problems in applied algebraic geometry. The first problem is to construct an algorithmically efficient approximation to the real part of the zero set of an exponential sum. We construct ...
    • Toward a Classification of the Ranks and Border Ranks of All (3,3,3) Trilinear Forms 
      Allums, Derek (2011-08-08)
      The study of the ranks and border ranks of tensors is an active area of research. By the example of determining the complexity of matrix multiplication I introduce the reader to the notion of the rank and border rank of a ...