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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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  • Scissors congruence and K-theory 
    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 ...
  • Geometric manipulation of light : from nonlinear optics to invisibility cloaks 
    Hashemi, Hila (Massachusetts Institute of Technology, 2012)
    In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ...
  • Eigenvalues and low energy eigenvectors of quantum many-body systems 
    Movassagh, Ramis (Massachusetts Institute of Technology, 2012)
    I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin systems on a line with an improvement on the notation. The rest of this thesis is divided into two parts. The first part ...
  • Modular invariance for vertex operator superalgebras 
    Van Ekeren, Jethro (Jethro William) (Massachusetts Institute of Technology, 2012)
    We generalize Zhu's theorem on modular invariance of characters of vertex operator algebras (VOAs) to the setting of vertex operator superalgebras (VOSAs) with rational, rather than integer, conformal weights. To recover ...
  • A classification of real and complex nilpotent orbits of reductive groups in terms of complex even nilpotent orbits 
    Speh, Peter (Peter Daniel) (Massachusetts Institute of Technology, 2012)
    Let g be a complex, reductive Lie algebra. We prove a theorem parametrizing the set of nilpotent orbits in g in terms of even nilpotent orbits of subalgebras of g and show how to determine these subalgebras and how to ...
  • The generalized Tate construction 
    Stroilova, Olga (Olga Y.) (Massachusetts Institute of Technology, 2012)
    The purpose of this work is give some field notes on exploring the idea that a generalized Tate construction tk reduces chromatic level in stable homotopy theory. The first parts introduce the construction and discuss ...
  • Geometric Langlands in prime characteristic 
    Chen, Tsao-Hsien (Massachusetts Institute of Technology, 2012)
    Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the ...
  • A free boundary problem inspired by a conjecture of De Giorgi 
    Kamburov, Nikola (Nikola Angelov) (Massachusetts Institute of Technology, 2012)
    We study global monotone solutions of the free boundary problem that arises from minimizing the energy functional I(u) = f lVul2 + V(U), where V(u) is the characteristic function of the interval (-1, 1). This functional ...
  • Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants 
    Preygel, Anatoly (Massachusetts Institute of Technology, 2012)
    The derived category of a hypersurface has an action by "cohomology operations" k[[beta]], deg[beta] = 2, underlying the 2-periodic structure on its category of singularities (as matrix factorizations). We prove a ...
  • Homological mirror symmetry for a Calabi-Yau hypersurface in projective space 
    Sheridan, Nicholas (Nicholas James) (Massachusetts Institute of Technology, 2012)
    This thesis is concerned with Kontsevich's Homological Mirror Symmetry conjecture. In Chapter 1, which is based on [1], we consider the n-dimensional pair of pants, which is defined to be the complement of n + 2 generic ...
  • Mean curvature flow self-shrinkers with genus and asymptotically conical ends 
    Møller, Niels Martin (Massachusetts Institute of Technology, 2012)
    This doctoral dissertation is on the theory of Minimal Surfaces and of singularities in Mean Curvature Flow, for smooth submanifolds Y" in an ambient Riemannian (n+ 1)-manifold Nn+1, including: (1) New asymptotically conical ...
  • Quantum geometric Langlands correspondence in positive characteristic: the GLN case 
    Travkin, Roman (Roman Mikhailovich) (Massachusetts Institute of Technology, 2012)
    Let C be a smooth connected projective curve of genus > 1 over an algebraically closed field k of characteristic p > 0, and c [epsilon] k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet the line bundle ...
  • Pattern avoidance for alternating permutations and reading words of tableaux 
    Lewis, Joel Brewster (Massachusetts Institute of Technology, 2012)
    We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of ...
  • Spectral asymptotics for coupled Dirac operators 
    Savale, Nikhil, Jr. (Nikhil A.) (Massachusetts Institute of Technology, 2012)
    In this thesis, we study the problem of asymptotic spectral flow for a family of coupled Dirac operators. We prove that the leading order term in the spectral flow on an n dimensional manifold is of order r n+1/2 followed ...
  • Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields 
    Morales, Alejandro Henry (Massachusetts Institute of Technology, 2012)
    In the first part of this thesis we study factorizations of the permutation (1; 2,..., n) into k factors of given cycle type. Using representation theory, Jackson obtained for each k an elegant formula for counting these ...
  • Free resolutions, combinatorics, and geometry 
    Sam, Steven V (Massachusetts Institute of Technology, 2012)
    Boij-Söderberg theory is the study of two cones: the first is the cone of graded Betti tables over a polynomial ring, and the second is the cone of cohomology tables of coherent sheaves over projective space. Each cone has ...
  • Symplectic cohomology and duality for the wrapped Fukaya Category 
    Ganatra, Sheel (Sheel Chandrakant) (Massachusetts Institute of Technology, 2012)
    Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from ...
  • Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations 
    Sohinger, Vedran (Massachusetts Institute of Technology, 2011)
    In this thesis, we study the growth of Sobolev norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a ...
  • Bordered Legendrian knots and sutured Legendrian invariants 
    Sivek, Steven (Steven W.) (Massachusetts Institute of Technology, 2011)
    In this thesis we apply techniques from the bordered and sutured variants of Floer homology to study Legendrian knots. First, given a front diagram for a Legendrian knot K in S₃ which has been split into several pieces, ...
  • Deformations of characters, metaplectic Whittaker functions, and the Yang-Baxter equation 
    Tabony, Sawyer James (Massachusetts Institute of Technology, 2011)
    Recently, unexpected connections have been discovered between characters of representations and lattice models in statistical mechanics. The bridge was first formed from Kuperberg's solution to the alternating sign matrix ...
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