Browsing by Author "Sottile, Frank"

Now showing items 1-20 of 41

    • Advanced Coding Techniques with Applications to Storage Systems 
      Nguyen, Phong Sy (2012-07-16)
      This dissertation considers several coding techniques based on Reed-Solomon (RS) and low-density parity-check (LDPC) codes. These two prominent families of error-correcting codes have attracted a great amount of interest ...
    • An Extension of Descartes' Rule of Signs to Multiple Variables, with Applications to Models of Biological Systems 
      Barton, Andrea (2023-04-17)
      Many biological systems are modeled mathematically using systems of differential equations. Descartes’ rule of signs is a common tool for analyzing these systems. In this thesis we explore a new perspective on Descartes’ ...
    • Codes for Distributed Machine Learning 
      Muthuveeru Subramaniam, Adarsh (2020-04-17)
      The problem considered is that of distributing machine learning operations of matrix multiplication and multivariate polynomial evaluation among computer nodes a.k.a worker nodes some of whom don’t return their outputs or ...
    • Computational Aspects of Galois Groups in Enumerative Geometry 
      Yahl, Thomas J. (2023-08-09)
      To an enumerative problem, one may associate a Galois group which encodes symmetries of the solutions to the problem. Galois groups of enumerative problems were first defined and studied by Jordan who considered them in ...
    • 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 ...
    • Discriminant coamoebas through homology 
      Passare, Mikael; Sottile, Frank (Journal of Commutative Algebra, 2013)
    • Equations for Chow Varieties, Their Secant Varieties and Other Varieties Arising in Complexity Theory 
      Guan, Yonghui (2016-05-24)
      The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Brill, Gordon, and others obtained set-theoretic equations for the Chow variety. I compute Brill's ...
    • G-Varieties and the Principal Minors of Symmetric Matrices 
      Oeding, Luke (2010-07-14)
      The variety of principal minors of nxn symmetric matrices, denoted Zn, can be described naturally as a projection from the Lagrangian Grassmannian. Moreover, Zn is invariant under the action of a group G C GL(2n) isomorphic ...
    • Gale duality for complete intersections 
      Bihan, Frédéric; Sottile, Frank (Annales de l'Institut Fourier, 2008)
    • Galois Groups of Schubert Problems 
      Martin Del Campo Sanchez, Abraham (2012-10-19)
      The Galois group of a Schubert problem is a subtle invariant that encodes intrinsic structure of its set of solutions. These geometric invariants are difficult to determine in general. However, based on a special position ...
    • Geometry and Representation Theory in the Study of Matrix Rigidity 
      Gesmundo, Fulvio (2017-04-20)
      The notion of matrix rigidity was introduced by L. Valiant in 1977. He proved a theorem that relates the rigidity of a matrix to the complexity of the linear map that it defines, and proposed to use this theorem to prove ...
    • Geometry of Feasible Spaces of Tensors 
      Qi, Yang (2013-07-17)
      Due to the exponential growth of the dimension of the space of tensors V_(1)⊗• • •⊗V_(n), any naive method of representing these tensors is intractable on a computer. In practice, we consider feasible subspaces ...
    • Goncarov Polynomials, Partition Lattices and Parking Sequences 
      Adeniran, Ayomikun Chukwuemeka (2020-06-01)
      Classical Goncarov polynomials arose in numerical analysis as a basis for the solutions of the Goncarov interpolation problem. These polynomials provide a natural algebraic tool in the enumerative theory of parking functions. ...
    • Hopf Structures on the Multiplihedra 
      Forcey, Stefan; Lauve, Aaron; Sottile, Frank (SIAM Journal on Discrete Mathematics, 2010)
    • Immanants, Tensor Network States and the Geometric Complexity Theory Program 
      Ye, Ke (2012-10-19)
      We study the geometry of immanants, which are polynomials on n^2 variables that are defined by irreducible representations of the symmetric group Sn. We compute stabilizers of immanants in most cases by computing Lie ...
    • Injectivity Properties of Generalized Wronski Map 
      Huang, Yanhe (2016-05-02)
      Given a complex vector space V, consider the quotient map of the image of the Plucker embedding of the Grassmannian of m-planes of V by a certain subspace of P ∧m V . Such maps generalize the classical Wronski maps on ...
    • Irrational Toric Varieties 
      Pir, Ata Firat (2018-08-27)
      Classical toric varieties are among the simplest objects in algebraic geometry. They arise in an elementary fashion as varieties parametrized by monomials whose exponents are a finite subset A of Zⁿ . They may also be ...
    • Lifting the Abstraction Level of Compiler Transformations 
      Tang, Xiaolong (2013-08-08)
      Production compilers implement optimizing transformation rules for built-in types. What justifies applying these optimizing rules is the axioms that hold for built-in types and the built-in operations supported by these ...
    • Local Cohomology: Combinatorics and D-Modules 
      Barrera III, Roberto (2017-08-04)
      In this thesis, we study combinatorial and D-module theoretic aspects of local cohomology. Viewing local cohomology from the point of view of A-hypergeometric systems, the quasidegree set of the non-top local cohomology ...
    • Multidimensional Parking Functions 
      Snider, Lauren Leigh (2023-04-26)
      Two multidimensional generalizations of Konheim and Weiss’ classical parking functions are the U -parking functions and the (p, q)-parking functions. Originating in Khare, Lorentz, and Yan’s study of bivariate Gonˇcarov ...