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Browsing Department of Mathematics by Issue Date

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Browsing Department of Mathematics by Issue Date

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  • Geneson, Jesse (Jesse T.) (Massachusetts Institute of Technology, 2015)
    Extremal functions of forbidden sequences and 0 - 1 matrices have applications to many problems in discrete geometry and enumerative combinatorics. We present a new computational method for deriving upper bounds on extremal ...
  • Iriarte Giraldo, Benjamin (Massachusetts Institute of Technology, 2015)
    This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertex-set with a totally ordered set, ...
  • Ostrev, Dimiter (Massachusetts Institute of Technology, 2015)
    We study optimal and nearly-optimal quantum strategies for non-local XOR games. First, we prove the following general result: for every non-local XOR game, there exists a set of relations with the properties: (1) a quantum ...
  • Harris, Daniel Martin (Massachusetts Institute of Technology, 2015)
    A decade ago, Yves Couder and coworkers discovered that millimetric droplets can walk on a vibrated fluid bath, and that these walking droplets or "walkers" display several features reminiscent of quantum particles. We ...
  • Wang, Guozhen, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2015)
    In this thesis, I study unstable homotopy theory with chromatic methods. Using the v, self maps provided by the Hopkins-Smith periodicity theorem, we can decompose the unstable homotopy groups of a space into its periodic ...
  • Mendelson, Dana Sydney (Massachusetts Institute of Technology, 2015)
    In the first part of this thesis we consider the defocusing nonlinear wave equation of power-type on R3. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In ...
  • Zhao, Yufei (Massachusetts Institute of Technology, 2015)
    We extend various fundamental combinatorial theorems and techniques from the dense setting to the sparse setting. First, we consider Szemerédi regularity lemma, a fundamental tool in extremal combinatorics. The regularity ...
  • Svaldi, Roberto (Massachusetts Institute of Technology, 2015)
    The Minimal Model Program (in short, MMP) aims at classifying projective algebraic varieties from a birational point of view. That means that starting from a projective algebraic variety X, [Delta] it is allowed to change ...
  • Potechin, Aaron H (Massachusetts Institute of Technology, 2015)
    Space complexity is the study of how much space/memory it takes to solve problems. Unfortunately, proving general lower bounds on space complexity is notoriously hard. Thus, we instead consider the restricted case of ...
  • Nandakumar, Vinoth (Massachusetts Institute of Technology, 2015)
    In this thesis, we will study three topics related to Springer theory (specifically, the geometry of the exotic nilpotent cone, and two-block Springer fibers), and stability conditions for category 0. In the first chapter, ...
  • Zhu, Xuwen, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2015)
    This thesis consists of three parts. In the first part, we study the eleven dimensional supergravity equations on B 7 x S 4 considered as an edge manifold. We compute the indicial roots of the linearized system using the ...
  • Wei, Wenzhe (Massachusetts Institute of Technology, 2015)
    In the thesis we propose a novel method for low rank matrix recovery. We study the framework using absolute deviation loss function and nuclear penalty. While nuclear norm penalty is widely utilized heuristic method for ...
  • Trongsiriwat, Wuttisak (Massachusetts Institute of Technology, 2015)
    In the first part, we study pattern avoidance and permutation statistics. For a set of patterns n and a permutation statistic st, let Fst/n ([Pi]; q) be the polynomial that counts st on the permutations avoiding all patterns ...
  • Shlapentokh-Rothman, Yakov (Massachusetts Institute of Technology, 2015)
    In this thesis we study wave and Klein-Gordon equations on Kerr exterior spacetimes. For the wave equation, we give a quantitative refinement and simple proofs of mode stability type statements on Kerr backgrounds in the ...
  • Watson, Samuel Stewart, 1986- (Massachusetts Institute of Technology, 2015)
    The study of two-dimensional statistical physics models leads naturally to the analysis of various conformally invariant mathematical objects, such as the Gaussian free field, the Schramm-Loewner evolution, and the conformal ...
  • Grinshpun, Andrey Vadim (Massachusetts Institute of Technology, 2015)
    A graph G is r-Ramsey minimal with respect to a graph H if every r-coloring of the edges of G yields a monochromatic copy of H, but the same is not true for any proper subgraph of G. The study of the properties of graphs ...
  • Zepeda-Núñ̃ez, Leonardo Andrés (Massachusetts Institute of Technology, 2015)
    In this thesis we develop a new family of fast and scalable algorithms to solve the 2D high-frequency Helmholtz equation in heterogeneous medium. The algorithms rely on a layered domain decomposition and a coupling between ...
  • Zeng, Yi, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2015)
    Lithium-ion battery is a family of rechargeable batteries with increasing importance that is closely related to everyone's daily life. However, despite its enormously wide applications in numerous areas, the mechanism of ...
  • Donovan, Michael Jack (Massachusetts Institute of Technology, 2015)
    In this thesis we study the Bousfield-Kan spectral sequence (BKSS) in the Quillen model category sCom of simplicial commutative FF₂ -algebras. We develop a theory of unstable operations for this BKSS and relate these ...
  • Glasman, Saul (Massachusetts Institute of Technology, 2015)
    This thesis is divided into two chapters. In the first, given symmetric monoidal oc-categories C and D, subject to mild hypotheses on D, we define an oc-categorical analog of the Day convolution symmetric monoidal structure ...
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