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Browsing Department of Mathematics by Title
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 2005)We describe a cooperad structure on the simplicial bar construction on a reduced operad of based spaces or spectra and, dually, an operad structure on the cobar construction on a cooperad. Further, we show that if the ...
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(Massachusetts Institute of Technology, 2013)This thesis mainly deals with the study of the category of admissible modules for the affine Kac-Moody algebra at the critical level, and the study of its center.
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(Massachusetts Institute of Technology, 2003)In this thesis, we introduce a notion of asymptotic stability for a holomorphic vector bundle with a global holomorphic section on a projective manifold. We prove that the special metric on the bundle studied by Bradlow ...
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(Massachusetts Institute of Technology, 2005)Our newly developing theory of bidimensional graph problems provides general techniques for designing efficient fixed-parameter algorithms and approximation algorithms for NP- hard graph problems in broad classes of graphs. ...
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(Massachusetts Institute of Technology, 2011)In this thesis, we investigate the birational geometry of the space of rational curves in various homogeneous spaces, with a focus on the quasi-map compactification induced by the Quot and Hyperquot functors. We first study ...
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(Massachusetts Institute of Technology, 2011)The Heegaard Floer hat invariant is defined on closed 3-manifolds, with a related invariant for 4-dimensional cobordisms, forming a 3+1 topological quantum field theory. Bordered Heegaard Floer homology generalizes this ...
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(Massachusetts Institute of Technology, 2011)In this thesis we apply techniques from the bordered and sutured variants of Floer homology to study Legendrian knots. First, given a front diagram for a Legendrian knot K in S₃ which has been split into several pieces, ...
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(Massachusetts Institute of Technology, 2005)In the framework of fibred cusp operators on a manifold X associated to a boundary fibration ... , the homotopy groups of the space ... of invertible smoothing perturbations of the identity are computed in terms of the ...
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(Massachusetts Institute of Technology, 2013)Coalescence of a liquid drop with a liquid bath can be prevented by vibration of the bath. In a certain parameter regime, a purely vertical bouncing motion may ensue. In another, this bouncing state is destabilized by the ...
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(Massachusetts Institute of Technology, 2008)Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we ...
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Boundary perturbation of the Laplace eigenvalues and applications to electron bubbles and polygons (Massachusetts Institute of Technology, 2003)We analyze the evolution of Laplace eigenvalues on a domain induced by the motion of the boundary. We apply our analysis to two problems: 1. We study the equilibrium and stability of electron bubbles. Electron bubbles are ...
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(Massachusetts Institute of Technology, 1976)
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(Massachusetts Institute of Technology, 1976)
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(Massachusetts Institute of Technology, 2011)In this thesis, we study the growth of Sobolev norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a ...
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(Massachusetts Institute of Technology, 2005)We provide two algorithms to solve branching from K to M for the real split reductive group of type A, one inductive and one related to semistandard Young tableaux. The results extend to branching from Ke to M Ke for the ...
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(Massachusetts Institute of Technology, 2007)The classical Brill-Noether theorems count the dimension of the family of maps from a general curve of genus g to non-degenerate curves of degree d in projective space Pr. These theorems can be extended to include ramification ...
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(Massachusetts Institute of Technology, 2009)Broken Lefschetz fibrations are a new way to depict smooth 4-manifolds and to investigate their topology; for instance, Perutz defines invariants of 4-manifolds by counting J-holomorphic sections of these fibrations. The ...
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(Massachusetts Institute of Technology, 1961)
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(Massachusetts Institute of Technology, 2001)This thesis will be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: ...
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