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Browsing Theses - Mathematics by Title

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  • Lipson, Mark (Mark Israel) (Massachusetts Institute of Technology, 2014)
    In the last few decades, the study of human history has been fundamentally changed by our ability to detect the signatures left within our genomes by adaptations, migrations, population size changes, and other processes. ...
  • Lee, Eun Soo, 1975- (Massachusetts Institute of Technology, 2003)
    The purpose of this thesis is proving conjectures in [1] on the Khovanov invariant. Khovanov invariant [6] is an invariant of (relatively) oriented links which is a cohomology theory over the cube of the resolutions of a ...
  • Tay, Kian Boon (Massachusetts Institute of Technology, 1994)
  • Sommers, Eric Nathan, 1971- (Massachusetts Institute of Technology, 1997)
  • Xue, Ting, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2010)
    Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p, g the Lie algebra of G and g* the dual vector space of g. This thesis is concerned with nilpotent orbits in g and g* ...
  • Xiao, Liang, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2009)
    In this thesis, I first systematically develop the theory of nonarchimedean differential modules, deducing fundamental theorems about the variation of generic radii of convergence for differential modules over polyannuli. ...
  • Chan, Daniel Sai-Ping, 1971- (Massachusetts Institute of Technology, 1999)
  • Angeltveit, Vigleik (Massachusetts Institute of Technology, 2006)
    Let A be an Ax ring spectrum. We give an explicit construction of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another family of polyhedra called cyclohedra. Using this construction ...
  • Patrick, David M., 1972- (Massachusetts Institute of Technology, 1997)
  • Chow, Chak-On, 1968- (Massachusetts Institute of Technology, 2001)
    The noncommutative symmetric functions Sym of Gelfand et al. give not only a lifting of the well-developed commutative theory of symmetric functions to the non-commutative level, but also relate the descent algebras of ...
  • Mendelson, Dana Sydney (Massachusetts Institute of Technology, 2015)
    In the first part of this thesis we consider the defocusing nonlinear wave equation of power-type on R3. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In ...
  • Watanabe, Shinya (Massachusetts Institute of Technology, 1995)
  • Lippert, Ross Adams (Massachusetts Institute of Technology, 1998)
  • Gorsich, David John, 1968- (Massachusetts Institute of Technology, 2000)
    Crucial in spatial interpolation of stochastic processes is the determination of the underlying dependency of the data. The dependency can be represented by an underlying covariogram, variogram, or generalized covariogram. ...
  • Ritter, Alexander F. (Alexander Friedrich) (Massachusetts Institute of Technology, 2009)
    Given an exact symplectic manifold, can we find topological constraints to the existence of exact Lagrangian submanifolds? I developed an approach using symplectic cohomology which provides such conditions for exact ...
  • Wei, Wenzhe (Massachusetts Institute of Technology, 2015)
    In the thesis we propose a novel method for low rank matrix recovery. We study the framework using absolute deviation loss function and nuclear penalty. While nuclear norm penalty is widely utilized heuristic method for ...
  • Burns, Jason Matthew (Massachusetts Institute of Technology, 2007)
    We give nontrivial upper and lower bounds for the total number of distinct degree sequences among all simple, unlabeled graphs on n vertices (graphical partitions on n vertices). Our upper bound is ... for some constant ...
  • Nigam, Mats S. (Mats Sandje), 1970- (Massachusetts Institute of Technology, 1999)
  • Lehmann, Brian (Brian Todd) (Massachusetts Institute of Technology, 2010)
    Suppose that X is a smooth variety and L is an effective divisor. One of the main goals of bi rational geometry is to understand the asymptotic behavior of the linear series... as m increases. The two most important features ...
  • Batson, Joshua (Massachusetts Institute of Technology, 2014)
    In this thesis, we use invariants inspired by quantum field theory to study the smooth topology of links in space and surfaces in space-time. In the first half, we use Khovanov homology to the study the relationship between ...
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