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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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  • Guillemin, Victor; Schaeffer, David (2013-02-07)
  • Suh, Uhi Rinn (Massachusetts Institute of Technology, 2013)
    The first part of the thesis provides three equivalent definitions of a classical finite W-algebra Wfin(g, f) and two equivalent definitions of a classical affine W-algebra W(g, f, k) associated to a Lie algebra g, a ...
  • Haugseng, Rune (Massachusetts Institute of Technology, 2013)
    The goal of this thesis is to begin to lay the foundations for a theory of enriched [infinity]categories. We introduce a definition of such objects, based on a non-symmetric version of Lurie's theory of [infinity]-operads. ...
  • 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 ...
  • Marberg, Eric (Eric Paul) (Massachusetts Institute of Technology, 2013)
    This thesis considers three topics related to the representations of Coxeter systems, their Hecke algebras, and related groups. The first topic concerns the construction of generalized involution models, as defined by Bump ...
  • Singh, Bhairav (Massachusetts Institute of Technology, 2013)
    One of the fundamental results in geometric representation theory is the geometric Satake equivalence, between the category of spherical perverse sheaves on the affine Grassmannian of a reductive group G and the category ...
  • Loh, Po-Ru (Massachusetts Institute of Technology, 2013)
    Rapid advances in next-generation sequencing technologies are revolutionizing genomics, with data sets at the scale of thousands of human genomes fast becoming the norm. These technological leaps promise to enable corresponding ...
  • Li, Nan, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2013)
    We studies two examples of polytope slices, hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart ...
  • Chiu, Jiawei (Massachusetts Institute of Technology, 2013)
    In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...
  • Clausen, Dustin (Dustin Tate) (Massachusetts Institute of Technology, 2013)
    Let X be a regular arithmetic curve or point (meaning a regular separated scheme of finite type over Z which is connected and of Krull dimension </= 1). We define a compactly-supported variant Kc(X) of the algebraic K-theory ...
  • 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 ...
  • Liang, Xiangdong, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2013)
    Capillary instability (Plateau-Rayleigh instability) has been playing an important role in experimental work such as multimaterial fiber drawing and multilayer particle fabrication. Motivated by complex multi-fluid geometries ...
  • Molác̆ek, Jan, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2013)
    Coalescence of a liquid drop with a liquid bath can be prevented by vibration of the bath. In a certain parameter regime, a purely vertical bouncing motion may ensue. In another, this bouncing state is destabilized by the ...
  • Horel, Geoffroy (Geoffroy Jean) (Massachusetts Institute of Technology, 2013)
    In this thesis, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad [epsilon]d of little d-dimensional disks, we show ...
  • 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 ...
  • Fortuna, Giorgia (Massachusetts Institute of Technology, 2013)
    This thesis mainly deals with the study of the category of admissible modules for the affine Kac-Moody algebra at the critical level, and the study of its center.
  • Khandhawit, Tirasan (Massachusetts Institute of Technology, 2013)
    In this thesis, we extend Manolescus and Kronheimer-Manolescus construction of Floer homotopy type to general 3-manifolds. This Floer homotopy type is a candidate for an object whose suitable homology groups recover Floer ...
  • 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 ...
  • Yun, Taedong (Massachusetts Institute of Technology, 2013)
    We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by Fomin- Greene-Reiner-Shimozono, and we extend this notion to ...
  • Ullman, John Richard (Massachusetts Institute of Technology, 2013)
    In this thesis, we analyze a variant of the slice spectral sequence of [HHR (or SSS) called the regular slice spectral sequence (or RSSS). This latter spectral sequence is defined using only the regular slice cells. We ...
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