Browsing Department of Mathematics by Title
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The BeilinsonBernstein localization theorem for the affine Grassmannian
(Massachusetts Institute of Technology, 2013)This thesis mainly deals with the study of the category of admissible modules for the affine KacMoody algebra at the critical level, and the study of its center. 
Bergman kernel and stability of holomorphic vector bundles with sections
(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 ... 
Betaensembles with covariance
(Massachusetts Institute of Technology, 2014)This thesis presents analytic samplers for the [beta]Wishart and [beta]MANOVA ensembles with diagonal covariance. These generalize the [beta]ensembles of DumitriuEdelman, Lippert, KillipNenciu, ForresterRains, and ... 
The bidimensionality theory and its algorithmic applications
(Massachusetts Institute of Technology, 2005)Our newly developing theory of bidimensional graph problems provides general techniques for designing efficient fixedparameter algorithms and approximation algorithms for NP hard graph problems in broad classes of graphs. ... 
Birational geometry of the space of rational curves in homogeneous varieties
(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 quasimap compactification induced by the Quot and Hyperquot functors. We first study ... 
The blowup formula for higher rank Donaldson invariants
(Massachusetts Institute of Technology, 2014)In this thesis, I study the relationship between the higher rank Donaldson invariants of a smooth 4manifold X and the invariants of its blowup X#CP2 . This relationship can be expressed in terms of a formal power series ... 
Bordered Heegaard Floer Homology and fourmanifolds with corners
(Massachusetts Institute of Technology, 2011)The Heegaard Floer hat invariant is defined on closed 3manifolds, with a related invariant for 4dimensional cobordisms, forming a 3+1 topological quantum field theory. Bordered Heegaard Floer homology generalizes this ... 
Bordered Legendrian knots and sutured Legendrian invariants
(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, ... 
Bott periodicity for fibred cusp operators
(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 ... 
Bouncing and walking droplets : towards a hydrodynamic pilotwave theory
(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 ... 
Boundaries of Ktypes in discrete series
(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 ... 
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 ... 
Boundary values and restrictions of generalized functions with applications
(Massachusetts Institute of Technology, 1976) 
Bounds for the nonlinear filtering problem.
(Massachusetts Institute of Technology, 1976) 
Bounds on extremal functions of forbidden patterns
(Massachusetts Institute of Technology, 2015)Extremal functions of forbidden sequences and 0  1 matrices have applications to many problems in discrete geometry and enumerative combinatorics. We present a new computational method for deriving upper bounds on extremal ... 
Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
(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 ... 
Branching from K to M for split classical groups
(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 ... 
BrillNoethertype theorems with a movable ramification point
(Massachusetts Institute of Technology, 2007)The classical BrillNoether theorems count the dimension of the family of maps from a general curve of genus g to nondegenerate curves of degree d in projective space Pr. These theorems can be extended to include ramification ... 
Broken Lefschetz fibrations, Lagrangian matching invariants and OzsváthSzabó invariants
(Massachusetts Institute of Technology, 2009)Broken Lefschetz fibrations are a new way to depict smooth 4manifolds and to investigate their topology; for instance, Perutz defines invariants of 4manifolds by counting Jholomorphic sections of these fibrations. The ... 
Brownian motions on a Riemannian manifold
(Massachusetts Institute of Technology, 1961)