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Browsing Department of Mathematics by Title
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(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 ...
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(Massachusetts Institute of Technology, 1997)
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(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 ...
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 1998)
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(Massachusetts Institute of Technology, 2000)
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(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 ...
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(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 ...
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(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 ...
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(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 ...
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(Massachusetts Institute of Technology, 1972)
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(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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(Massachusetts Institute of Technology, 1997)
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(Massachusetts Institute of Technology, 2003)In this thesis, I study pseudo-holomorphic curves in symplectisation of the unit cotangent bundle of a Riemann surface of genus greater than 1. The contact form and compatible almost complex structure are both constructed ...
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(Massachusetts Institute of Technology, 1979)
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(Massachusetts Institute of Technology, 2009)This thesis has two parts. In Part I, we present the results of a combined experimental and theoretical investigation of the vertical impact of spheres on a water surface. Particular attention is given to characterizing ...
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(Massachusetts Institute of Technology, 1994)
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(Massachusetts Institute of Technology, 2005)In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the "strategy set") whose costs vary over time. After T trials, the ...
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(Massachusetts Institute of Technology, 1993)
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(Massachusetts Institute of Technology, 2007)We develop the basic theory of quasi-categories (a.k.a. weak Kan complexes or ([infinity], 1)- categories as in [BV73], [Joy], [Lur06]) from first principles, i.e. without reference to model categories or other ideas from ...
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