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Browsing Mathematics - Ph.D. / Sc.D. by Issue Date

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Browsing Mathematics - Ph.D. / Sc.D. by Issue Date

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  • Lin, Francesco Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2016)
    In this thesis we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold ...
  • Boger, D. (Dorin) (Massachusetts Institute of Technology, 2016)
    Let G be a reductive group over a field k = k. Let P be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a ...
  • 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 ...
  • Liu, Zihan Hans (Massachusetts Institute of Technology, 2016)
    In this thesis, we will introduce a notion of index of shrinkers of the mean curvature flow. We will then prove a gap theorem for the index of rotationally symmetric immersed shrinkers in R3, namely, that such shrinkers ...
  • Fei, Teng, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2016)
    The Strominger system is a system of partial differential equations describing the geometry of compactifications of heterotic superstrings with flux. Mathematically it can be viewed as a generalization of Ricci-flat metrics ...
  • Chang, Jui-En (Massachusetts Institute of Technology, 2016)
    This thesis contains two of my projects. Chapter 1 and 2 describe the behavior of 1-dimensional [lambda]-self shrinkers, which are also known as [lambda]-curves in other literature. Chapter 3 and 4 focus on the estimation ...
  • Viscardi, Michael (Massachusetts Institute of Technology, 2016)
    Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new ...
  • Srinivasan, Padmavathi (Massachusetts Institute of Technology, 2016)
    This thesis consists of two parts. In part one of this thesis, we study the relationship between the Artin conductor and the minimal discriminant of a hyperelliptic curve defined over the fraction field K of a discrete ...
  • Moll, Alexander (Alexander Christian Vincent) (Massachusetts Institute of Technology, 2016)
    Stanley's Cauchy identity for Jack symmetric functions defines a Jack measure, a model random partitions for every analytic real function v(w) on the unit circle and parameters E2 < 0 < E1. Jacks are eigenfunctions of the ...
  • Mangoubi, Oren (Oren Rami) (Massachusetts Institute of Technology, 2016)
    This thesis presents applications of differential geometry and graph theory to the design and analysis of Markov chain Monte Carlo (MCMC) algorithms. MCMC algorithms are used to generate samples from an arbitrary probability ...
  • Hortsch, Ruthi (Massachusetts Institute of Technology, 2016)
    Because many invariants and properties of elliptic curves are difficult to understand directly, the study of arithmetic statistics instead looks at what happens "on average", using heights to make this notion rigorous. ...
  • 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 ...
  • 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 ...
  • Engel Shaposhnik, Efrat (Massachusetts Institute of Technology, 2016)
    This thesis consists of two parts. In the first part we count antichains of interval orders and in particular semiorders. We associate a Dyck path to each interval order, and give a formula for the number of antichains of ...
  • Lee, Yin Tat (Massachusetts Institute of Technology, 2016)
    In this thesis, we revisit three algorithmic techniques: sparsification, cutting and collapsing. We use them to obtain the following results on convex and combinatorial optimization: --Linear Programming: We obtain the ...
  • Grinberg, Darij (Massachusetts Institute of Technology, 2016)
    In 1983, Ira Gessel introduced the ring of quasisymmetric functions (QSym), an extension of the ring of symmetric functions and nowadays one of the standard examples of a combinatorial Hopf algebra. In this thesis, I ...
  • Vaintrob, Dmitry (Massachusetts Institute of Technology, 2016)
    Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building ...
  • Sun, Yi, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2016)
    We present a collection of results on the relationship between intertwining operators for quantum groups and eigenfunctions for quantum integrable systems. First, we study the Etingof-Kirillov Jr. expression of Macdonald ...
  • Berchenko-Kogan, Yakov (Massachusetts Institute of Technology, 2016)
    We develop an analog of the harmonic replacement technique of Colding and Minicozzi in the gauge theory context. The idea behind harmonic replacement dates back to Schwarz and Perron, and the technique involves taking a ...
  • Binder, John (John Robert) (Massachusetts Institute of Technology, 2016)
    This thesis examines questions related to the growth of fields of rationality of cuspidal automorphic representations in families. Specifically, if F is a family of cuspidal automorphic representations with fixed central ...
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