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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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  • Knizel, Alisa (Massachusetts Institute of Technology, 2017)
    In the thesis we explore and develop two different approaches to the study of random tiling models. First, we consider tilings of a hexagon by rombi, viewed as 3D random stepped surfaces with a measure proportional to ...
  • Rush, David B., Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2017)
    Let G be a connected complex reductive algebraic group with Lie algebra g. The Lusztig-Vogan bijection relates two bases for the bounded derived category of G-equivariant coherent sheaves on the nilpotent cone 11 of g. One ...
  • Shah, Jay (Jay Hungfai Gautam) (Massachusetts Institute of Technology, 2017)
    We develop foundations for the category theory of [infinity]-categories parametrized by a base occategory. Our main contribution is a theory of parametrized homotopy limits and colimits, which recovers and extends the ...
  • Lovász, László Miklós (Massachusetts Institute of Technology, 2017)
    In this thesis, we analyze the regularity method pioneered by Szemerédi, and also discuss one of its prevalent applications, the removal lemma. First, we prove a new lower bound on the number of parts required in a version ...
  • Finucane, Hilary Kiyo (Massachusetts Institute of Technology, 2017)
    In this thesis, I introduce new methods for learning about diseases and traits from genetic data. First, I introduce a method for partitioning heritability by functional annotation from genome-wide association summary ...
  • Carpentier, Sylvain, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2017)
    A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite ...
  • Yang, Ben, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2017)
    Incidence geometry is the study of the intersection patterns of simple geometric objects. One of the breakthroughs in this field is the polynomial partitioning technique introduced by Guth and Katz. In this thesis, I will ...
  • Sun, Xin, Ph. D. Massachusetts Institute of Technology. Department of Mathematics (Massachusetts Institute of Technology, 2017)
    In this thesis, we study the mating of trees approach to Liouville quantum gravity decorated with SLE curves and its application to the scaling limit theory of decorated random planar maps. We focus on the less investigated ...
  • Nardin, Denis, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2017)
    Let G be a finite group. The homotopy theory of topological spaces with an action of G has provided important applications in many parts of homotopy theory and geometry. An especially important role has been played by the ...
  • Lodhia, Asad (Massachusetts Institute of Technology, 2017)
    The behavior of the spectrum of a large random matrix is a topic of great interest in probability theory and statistics. At a global level, the limiting spectra of certain random matrix models have been known for some time. ...
  • Liu, Xue (Mathematician) (Massachusetts Institute of Technology, 2017)
    This thesis contains several results on the connectedness of Baues complexes and flip graphs, which are topological spaces modeling certain sets coming from geometric combinatorics. These sets include the triangulations ...
  • Harman, Nate (Nate Reid) (Massachusetts Institute of Technology, 2017)
    We study the asymptotic behavior of the representation theory of symmetric groups Sn, in positive characteristic as n grows to [infinity], with the goal of understanding and generalizing the Deligne categories Rep(St) as ...
  • Farber, Miriam, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2017)
    This thesis consists of three parts. In the first chapter we discuss arrangements of equal minors of totally positive matrices. More precisely, we investigate the structure of equalities and inequalities between the minors. ...
  • Fan, Chenjie (Massachusetts Institute of Technology, 2017)
    In this thesis, we investigate the long time behavior of focusing mass critical nonlinear Schrödinger equation (NLS). We will focus on the singularity formation and long time asymptotics. To be specific, there are two parts ...
  • Vladu, Adrian Valentin (Massachusetts Institute of Technology, 2017)
    In this thesis, we build connections between classic methods from convex optimization and the modern toolkit from the fast Laplacian solver literature, in order to make progress on a number of fundamental algorithmic ...
  • Yu, Yun William (Massachusetts Institute of Technology, 2017)
    Disparate biological datasets often exhibit similar well-defined structure; efficient algorithms can be designed to exploit this structure. In this doctoral thesis, we present a framework for similarity search based on ...
  • Wang, Menglu (Massachusetts Institute of Technology, 2017)
    Consider an instance h of the Gaussian free field on a simply connected domain ... We study several properties of the level lines: continuity, monotonicity, reversibility and target-independence ... In the second part, we ...
  • Thompson, Daniel (Daniel Craig) (Massachusetts Institute of Technology, 2017)
    This thesis studies the representation theory of Cherednik algebras associated to a complex algebraic varieties which carries the action of a finite group. First, we prove that the Knizhnik-Zamolodchikov functor from the ...
  • Bavarian, Mohammad (Massachusetts Institute of Technology, 2017)
    Parallel repetition is a fundamental operation for amplifying the hardness inherent in multiplayer games. Through the efforts of many researchers in the past two decades (e.g. Feige, Kilian, Raz, Holentstein, Rao, Braverman, ...
  • 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 ...
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