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Browsing Theses - Dept. of Mathematics by Title

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Browsing Theses - Dept. of Mathematics by Title

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  • Geometric algorithms for reconfigurable structures 
    Benbernou, Nadia M (Massachusetts Institute of Technology, 2011)
    In this thesis, we study three problems related to geometric algorithms of reconfigurable structures. In the first problem, strip folding, we present two universal hinge patterns for a strip of material that enable the ...
  • Geometric and algebraic properties of polyomino tilings 
    Korn, Michael Robert, 1978- (Massachusetts Institute of Technology, 2004)
    In this thesis we study tilings of regions on the square grid by polyominoes. A polyomino is any connected shape formed from a union of grid cells, and a tiling of a region is a collection of polyominoes lying in the region ...
  • Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients 
    Rassart, Étienne, 1975- (Massachusetts Institute of Technology, 2004)
    Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and Littlewood-Richardson coefficients (the type A weight multiplicities and Clebsch-Gordan coefficients). ...
  • Geometric Langlands in prime characteristic 
    Chen, Tsao-Hsien (Massachusetts Institute of Technology, 2012)
    Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the ...
  • Geometric manipulation of light : from nonlinear optics to invisibility cloaks 
    Hashemi, Hila (Massachusetts Institute of Technology, 2012)
    In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ...
  • Geometric quantization and dynamical constructions on the space of Kähler metrics 
    Rubinstein, Yanir Akiva (Massachusetts Institute of Technology, 2008)
    This Thesis is concerned with the study of the geometry and structure of the space of Kihler metrics representing a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a ...
  • A geometric theory of outliers and perturbation 
    Dunagan, John D. (John David), 1976- (Massachusetts Institute of Technology, 2002)
    We develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a ...
  • The geometry and topology of quotient varieties 
    Hu, Yi (Massachusetts Institute of Technology, 1991)
  • Geometry of cone-beam reconstruction 
    Yang, Xiaochun, 1971- (Massachusetts Institute of Technology, 2002)
    Geometry is the synthetic tool we use to unify all existing analytical cone-beam reconstruction methods. These reconstructions are based on formulae derived by Tuy [Tuy, 1983], Smith [Smith, 1985] and Grangeat [Grangeat, ...
  • Geometry of Ricci-flat Kähler manifolds and some counterexamples 
    Božin, Vladimir, 1973- (Massachusetts Institute of Technology, 2004)
    In this work, we study geometry of Ricci-flat Kähler manifolds, and also provide some counterexample constructions. We study asymptotic behavior of complete Ricci-flat metrics at infinity and consider a construction of ...
  • Geometry of river networks 
    Dodds, Peter Sheridan, 1969- (Massachusetts Institute of Technology, 2000)
  • The geometry of the generic line complex 
    Sher, Joshua S. (Joshua Simon) (Massachusetts Institute of Technology, 1995)
  • Goodwillie calculus and algebras over a spectral operad 
    Pereira, Luis Alexandre Meira Fernandes Alves (Massachusetts Institute of Technology, 2013)
    The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that ...
  • The Gowers norm in the testing of Boolean functions 
    Chen, Victor Yen-Wen (Massachusetts Institute of Technology, 2009)
    A property tester is a fast, randomized algorithm that reads only a few entries of the input, and based on the values of these entries, it distinguishes whether the input has a certain property or is "different" from any ...
  • Graded rings, modules and algebras. 
    Mendelssohn, Marvin (Massachusetts Institute of Technology, 1970)
  • Grammar for vision. 
    Shiman, Leon Gardner (Massachusetts Institute of Technology, 1975)
  • Graph polynomials and statistical physics 
    Kim, Jae Ill, S.M. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2007)
    We present several graph polynomials, of which the most important one is the Tutte polynomial. These various polynomials have important applications in combinatorics and statistical physics. We generalize the Tutte polynomial ...
  • Graphs, matrices, and populations : linear algebraic techniques in theoretical computer science and population genetics 
    Levin, Alex, Ph. D. (Alexander). Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2013)
    In this thesis, we present several algorithmic results for problems in spectral graph theory and computational biology. The first part concerns the problem of spectral sparsification. It is known that every dense graph can ...
  • Gröbner bases in rational homotopy theory 
    Lee, Wai Kei Peter (Massachusetts Institute of Technology, 2008)
    The Mayer-Vietoris sequence in cohomology has an obvious Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. ...
  • The heat kernel for manifolds with conic singularities 
    Mooers, Edith (Massachusetts Institute of Technology, 1996)
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