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Browsing Department of Mathematics by Title

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  • Deshpande, Amit Jayant (Massachusetts Institute of Technology, 2007)
    Can one compute a low-dimensional representation of any given data by looking only at its small sample, chosen cleverly on the fly? Motivated by the above question, we consider the problem of low-rank matrix approximation: ...
  • Christiansen, Tanya J. (Tanya Julie) (Massachusetts Institute of Technology, 1993)
  • Andrews, Matthew (Massachusetts Institute of Technology, 1997)
  • Bressler, Paul (Massachusetts Institute of Technology, 1989)
  • Entova Aizenbud, Inna (Massachusetts Institute of Technology, 2016)
    This thesis gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with a distinguished non-zero vector 1) we ...
  • Zakharevich, Inna (Inna Ilana) (Massachusetts Institute of Technology, 2012)
    In this thesis we develop a version of classical scissors congruence theory from the perspective of algebraic K-theory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed ...
  • Rippel, Oren (Massachusetts Institute of Technology, 2016)
    In machine learning, the choice of space in which to represent our data is of vital importance to their effective and efficient analysis. In this thesis, we develop approaches to address a number of problems in representation ...
  • Zaff, David Benjamin (Massachusetts Institute of Technology, 1987)
  • Boyle, Elette Chantae (Massachusetts Institute of Technology, 2013)
    A secure multi-party computation (MPC) protocol for computing a function f allows a group of parties to jointly evaluate f over their private inputs, such that a computationally bounded adversary who corrupts a subset of ...
  • Blanchette, François Alain, 1978- (Massachusetts Institute of Technology, 2003)
    We study the interaction between settling particles and a stratified ambient in a variety of contexts. We first study the generation of large scale fluid motions by the localised release of a finite mass of particles in ...
  • Lopes, William Manuel (Massachusetts Institute of Technology, 2010)
    In this thesis I study the Seiberg-Witten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the Seiberg-Witten ...
  • Nguyen, Timothy (Timothy Chieu) (Massachusetts Institute of Technology, 2011)
    In this thesis, we undertake an in-depth study of the Seiberg-Witten equations on manifolds with boundary. We divide our study into three parts. In Part One, we study the Seiberg-Witten equations on a compact 3-manifold ...
  • Granja, Gustavo, 1971- (Massachusetts Institute of Technology, 1997)
  • Guang, Qiang, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2016)
    We study singularity models of mean curvature flow ("MCF") and their generalizations. In the first part, we focus on rigidity and curvature estimates for self-shrinkers. We give a rigidity theorem proving that any self-shrinker ...
  • Wang, Lu, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2011)
    In this thesis, first, joint with Longzhi Lin, we establish estimates for the harmonic map heat flow from the unit circle into a closed manifold, and use it to construct sweepouts with the following good property: each ...
  • Halldórsson, Höskuldur Pétur (Massachusetts Institute of Technology, 2013)
    In the first part of this thesis, we give a classification of all self-similar solutions to the curve shortening flow in the Euclidean plane R² and discuss basic properties of the curves. The problem of finding the curves ...
  • Česnavičius, Kęstutis (Massachusetts Institute of Technology, 2014)
    Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined ...
  • Lipyanskiy, Maksim (Massachusetts Institute of Technology, 2008)
    This dissertation is concerned with the foundations of a new approach to Floer theory. As opposed to the traditional approach, which can be viewed as a generalization of Morse theory to an infinite dimensional setting, our ...
  • Tesler, Glenn Paul (Massachusetts Institute of Technology, 1995)
  • Murchison, Clinton Williams, 1895-1969 (Massachusetts Institute of Technology, 1947)
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