Browsing Mathematics  Ph.D. / Sc.D. by Title
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Obstructions to rational and integral points
(Massachusetts Institute of Technology, 2018)In this thesis, I study two examples of obstructions to rational and integral points on varieties. The first concerns the Sunit equation, which asks for solutions to x + y = 1 with x and y both Sunits, or units in Z = ... 
Obstructions to slicing knots and splitting links
(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 spacetime. In the first half, we use Khovanov homology to the study the relationship between ... 
Odd dimensional symplectic manifolds by Zhenqi He.
(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 ... 
The [omega]spectrum for BrownPeterson cohomology,
(Massachusetts Institute of Technology, 1972) 
On a class of temporally nonhomogeneous Markov processes and their relationship to infinite particle gases.
(Massachusetts Institute of Technology, 1966) 
On affine embeddings of reductive groups
(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, ... 
On bubble dynamics and gas dynamics in open tubes
(Massachusetts Institute of Technology, 1997) 
On contact homology of the unit cotangent bundle of a Riemann surface with genus greater than one
(Massachusetts Institute of Technology, 2003)In this thesis, I study pseudoholomorphic 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 ... 
On evasiveness, permutation embeddings, and mappings on sequences.
(Massachusetts Institute of Technology, 1975) 
On falling spheres : the dynamics of water entry and descent along a flexible beam
(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 ... 
On folding and unfolding with linkages and origami
(Massachusetts Institute of Technology, 2016)We revisit foundational questions in the kinetic theory of linkages and origami, investigating their folding/unfolding behaviors and the computational complexity thereof. In Chapter 2, we exactly settle the complexity of ... 
On geometric constructions of the universal enveloping algebra U(slnÌ³)
(Massachusetts Institute of Technology, 1994) 
On integral equations, their solution by iteration and analytic continuation
(Massachusetts Institute of Technology, 1950) 
On local representations of graphs and networks
(Massachusetts Institute of Technology, 1993) 
On long time dynamic and singularity formation of NLS
(Massachusetts Institute of Technology, 2017)In this thesis, we investigate the long time behavior of focusing mass critical nonlinear Schrödinger equation (NLS). We will focus on the singularity formation and long time asymptotics. To be specific, there are two parts ... 
On moduli stacks of finite group schemes
(Massachusetts Institute of Technology, 2000) 
On planar rational cuspidal curves
(Massachusetts Institute of Technology, 2014)This thesis studies rational curves in the complex projective plane that are homeomorphic to their normalizations. We derive some combinatorial constraints on such curves from a result of BorodzikLivingston in HeegaardFloer ... 
On quasicategories as a foundation for higher algebraic stacks
(Massachusetts Institute of Technology, 2007)We develop the basic theory of quasicategories (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 ... 
On quaternionic line bundles
(Massachusetts Institute of Technology, 1999) 
On quintic surfaces of general type
(Massachusetts Institute of Technology, 1984)