Browsing Mathematics - Ph.D. / Sc.D. by Title
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Browsing Mathematics - Ph.D. / Sc.D. by Title
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(Massachusetts Institute of Technology, 2000)
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 2013)The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that ...
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(Massachusetts Institute of Technology, 2009)A property tester is a fast, randomized algorithm that reads only a few entries of the input, and based on the values of these entries, it distinguishes whether the input has a certain property or is "different" from any ...
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(Massachusetts Institute of Technology, 2013)In this thesis, we present several algorithmic results for problems in spectral graph theory and computational biology. The first part concerns the problem of spectral sparsification. It is known that every dense graph can ...
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(Massachusetts Institute of Technology, 2008)The Mayer-Vietoris sequence in cohomology has an obvious Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. ...
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(Massachusetts Institute of Technology, 1996)
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 1961)
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(Massachusetts Institute of Technology, 1993)
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(Massachusetts Institute of Technology, 2005)In this thesis, we derive the asymptotic expansion of the Kiihler-Einstein metrics on certain quasi-projective varieties, which can be compactified by adding a divisor with simple normal crossings. The weighted Cheng-Yau ...
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(Massachusetts Institute of Technology, 2011)We present two recent parallel programming languages, PetaBricks and Julia, and demonstrate how we can use these two languages to re-examine classic numerical algorithms in new approaches for high-performance computing. ...
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(Massachusetts Institute of Technology, 2008)Preprojective algebras [Pi]q of quivers Q were introduced by Gelfand and Ponomarev in 1979 in order to provide a model for quiver representations (in the special case of finite Dynkin quivers). They showed that in the ...
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(Massachusetts Institute of Technology, 1986)
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(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 ...
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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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