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Browsing Mathematics - Ph.D. / Sc.D. by Title

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Browsing Mathematics - Ph.D. / Sc.D. by Title

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  • 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 ...
  • Watanabe, Shinya (Massachusetts Institute of Technology, 1995)
  • Lippert, Ross Adams (Massachusetts Institute of Technology, 1998)
  • Gorsich, David John, 1968- (Massachusetts Institute of Technology, 2000)
  • 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 ...
  • 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 ...
  • He, Zhenqi, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2010)
    In this thesis, we introduce the odd dimensional symplectic manifolds. In the first half we study the Hodge theory on the basic symplectic manifolds. We can define two cohomology theories on them, the standard basic de ...
  • Wilson, Walter Stephen (Massachusetts Institute of Technology, 1972)
  • Hyun, Yoonsuk (Massachusetts Institute of Technology, 2011)
    In this thesis, we study the properties and the classification of embeddings of homogeneous spaces, especially the case of affine normal embeddings of reductive groups. We might guess that as in the case of toric varieties, ...
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