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Browsing Department of Mathematics by Title

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  • Banach categories with conjugation. 
    Recht, Lázaro (Massachusetts Institute of Technology, 1969)
  • B and D analogues of stable Schubert polynomials and related insertion algorithms 
    Lam, Tao Kai (Massachusetts Institute of Technology, 1995)
  • Bar constructions for topological operads and the Goodwillie derivatives of the identity 
    Ching, Michael (Michael Comyn) (Massachusetts Institute of Technology, 2005)
    We describe a cooperad structure on the simplicial bar construction on a reduced operad of based spaces or spectra and, dually, an operad structure on the cobar construction on a cooperad. Further, we show that if the ...
  • The Beilinson-Bernstein localization theorem for the affine Grassmannian 
    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.
  • Bergman kernel and stability of holomorphic vector bundles with sections 
    Wang, Lijing, 1975- (Massachusetts Institute of Technology, 2003)
    In this thesis, we introduce a notion of asymptotic stability for a holomorphic vector bundle with a global holomorphic section on a projective manifold. We prove that the special metric on the bundle studied by Bradlow ...
  • Beta-ensembles with covariance 
    Dubbs, Alexander (Massachusetts Institute of Technology, 2014)
    This thesis presents analytic samplers for the [beta]-Wishart and [beta]-MANOVA ensembles with diagonal covariance. These generalize the [beta]-ensembles of Dumitriu-Edelman, Lippert, Killip-Nenciu, Forrester-Rains, and ...
  • The bidimensionality theory and its algorithmic applications 
    Hajiaghayi, MohammadTaghi (Massachusetts Institute of Technology, 2005)
    Our newly developing theory of bidimensional graph problems provides general techniques for designing efficient fixed-parameter algorithms and approximation algorithms for NP- hard graph problems in broad classes of graphs. ...
  • Birational geometry of the space of rational curves in homogeneous varieties 
    Venkatram, Kartik (Kartik Swaminathan) (Massachusetts Institute of Technology, 2011)
    In this thesis, we investigate the birational geometry of the space of rational curves in various homogeneous spaces, with a focus on the quasi-map compactification induced by the Quot and Hyperquot functors. We first study ...
  • The blowup formula for higher rank Donaldson invariants 
    Culler, Lucas Howard (Massachusetts Institute of Technology, 2014)
    In this thesis, I study the relationship between the higher rank Donaldson invariants of a smooth 4-manifold X and the invariants of its blowup X#CP2 . This relationship can be expressed in terms of a formal power series ...
  • Bordered Heegaard Floer Homology and four-manifolds with corners 
    Brown, Tova Helen Fell (Massachusetts Institute of Technology, 2011)
    The Heegaard Floer hat invariant is defined on closed 3-manifolds, with a related invariant for 4-dimensional cobordisms, forming a 3+1 topological quantum field theory. Bordered Heegaard Floer homology generalizes this ...
  • 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, ...
  • Bott periodicity for fibred cusp operators 
    Rochon, Frédéric, 1978- (Massachusetts Institute of Technology, 2005)
    In the framework of fibred cusp operators on a manifold X associated to a boundary fibration ... , the homotopy groups of the space ... of invertible smoothing perturbations of the identity are computed in terms of the ...
  • Bouncing and walking droplets : towards a hydrodynamic pilot-wave theory 
    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 ...
  • Boundaries of K-types in discrete series 
    Havlíčková, Markéta (Massachusetts Institute of Technology, 2008)
    Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we ...
  • Boundary perturbation of the Laplace eigenvalues and applications to electron bubbles and polygons 
    Greenfield, Pavel, 1974- (Massachusetts Institute of Technology, 2003)
    We analyze the evolution of Laplace eigenvalues on a domain induced by the motion of the boundary. We apply our analysis to two problems: 1. We study the equilibrium and stability of electron bubbles. Electron bubbles are ...
  • Boundary values and restrictions of generalized functions with applications 
    Reitano, Robert Richard (Massachusetts Institute of Technology, 1976)
  • Bounds for the nonlinear filtering problem. 
    Klebanoff, Victor Franklin (Massachusetts Institute of Technology, 1976)
  • Bounds on extremal functions of forbidden patterns 
    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 ...
  • 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 ...
  • Branching from K to M for split classical groups 
    McCarthy, Nicholas (Nicholas Aaron) (Massachusetts Institute of Technology, 2005)
    We provide two algorithms to solve branching from K to M for the real split reductive group of type A, one inductive and one related to semistandard Young tableaux. The results extend to branching from Ke to M Ke for the ...
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