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Browsing Theses - Mathematics by Title
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(Massachusetts Institute of Technology, 1998)
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(Massachusetts Institute of Technology, 2001)We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal ...
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(Massachusetts Institute of Technology, 2002)In this thesis, I establish a homotopy equivalence between the matroid Grassmannian [parallel] MacP(k, n) [parallel] and the real Grassmannian G(k, n) of k-planes in [Real set]n. This is accomplished by finding a Schubert ...
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(Massachusetts Institute of Technology, 1998)
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(Massachusetts Institute of Technology, 2006)We present a combined experimental and theoretical investigation of the numerous hydrodynamic propulsion mechanisms employed by water-walking arthropods (insects and spiders). In our experimental study, high speed ...
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(Massachusetts Institute of Technology, 1976)
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(Massachusetts Institute of Technology, 2006)In this thesis, I consider hyper-Kähler manifolds of complex dimension 4 which are fibrations. It is known that the fibers are abelian varieties and the base is P2. We assume that the general fiber is isomorphic to a product ...
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(Massachusetts Institute of Technology, 2011)In this thesis, we address two problems involving partial differential equations. In the first problem, we reformulate the incompressible Navier-Stokes equations into an equivalent pressure Poisson system. The new system ...
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(Massachusetts Institute of Technology, 1997)
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(Massachusetts Institute of Technology, 2011)In this thesis, I explore aspects of a new jet shape - N-subjettiness - designed to identify boosted hadronically-decaying objects (with a particular focus on tagging top quarks) at particle accelerators such as the Large ...
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(Massachusetts Institute of Technology, 1970)
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(Massachusetts Institute of Technology, 2006)In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weakly-scattered theory. Using this predecessor function, we improve a recent bounding result by Sacks ...
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(Massachusetts Institute of Technology, 1962)
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(Massachusetts Institute of Technology, 2010)In this thesis, I investigate the index of Callias type operators on asymptotically conic manifolds (also known as asymptotically locally Euclidean manifolds or scattering manifolds) and give an application to the moduli ...
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(Massachusetts Institute of Technology, 2008)The classical transport theory cannot explain the experimental behavior of electrochemical systems in the extreme operating conditions required by modern microfluidics devices. Some experimental puzzles include strange ...
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(Massachusetts Institute of Technology, 2010)In recent work of Baas-Dundas-Richter-Rognes, the authors introduce the notion of the K- theory of a bimonoidal category R, and show that it is equivalent to the algebraic K-theory space of the ring spectrum KR. In this ...
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(Massachusetts Institute of Technology, 1998)
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(Massachusetts Institute of Technology, 2002)The central focus of my thesis is to study the instability jets of various complexity by analyzing the linear and nonlinear dynamics. We applied this methodology to four different situations in order to learn the following. ...
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(Massachusetts Institute of Technology, 2011)We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to ...
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(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 ...
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