Browsing Department of Mathematics by Title
Now showing items 652671 of 824

Scissors congruence and Ktheory
(Massachusetts Institute of Technology, 2012)In this thesis we develop a version of classical scissors congruence theory from the perspective of algebraic Ktheory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed ... 
Sculpting representations for deep learning
(Massachusetts Institute of Technology, 2016)In machine learning, the choice of space in which to represent our data is of vital importance to their effective and efficient analysis. In this thesis, we develop approaches to address a number of problems in representation ... 
Secondary instability in Ekman boundary flow by David B. Zaff.
(Massachusetts Institute of Technology, 1987) 
Secure multiparty protocols under a modern lens
(Massachusetts Institute of Technology, 2013)A secure multiparty computation (MPC) protocol for computing a function f allows a group of parties to jointly evaluate f over their private inputs, such that a computationally bounded adversary who corrupts a subset of ... 
Sedimentation in a stratified ambient
(Massachusetts Institute of Technology, 2003)We study the interaction between settling particles and a stratified ambient in a variety of contexts. We first study the generation of large scale fluid motions by the localised release of a finite mass of particles in ... 
The SeibergWitten equations on a surface times a circle
(Massachusetts Institute of Technology, 2010)In this thesis I study the SeibergWitten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the SeibergWitten ... 
The SeibergWitten equations on manifolds with boundary
(Massachusetts Institute of Technology, 2011)In this thesis, we undertake an indepth study of the SeibergWitten equations on manifolds with boundary. We divide our study into three parts. In Part One, we study the SeibergWitten equations on a compact 3manifold ... 
Self maps of quaternionic projective spaces
(Massachusetts Institute of Technology, 1997) 
Selfshrinkers and translating solitons of mean curvature flow
(Massachusetts Institute of Technology, 2016)We study singularity models of mean curvature flow ("MCF") and their generalizations. In the first part, we focus on rigidity and curvature estimates for selfshrinkers. We give a rigidity theorem proving that any selfshrinker ... 
Selfshrinkers of mean curvature flow and harmonic map heat flow with rough boundary data
(Massachusetts Institute of Technology, 2011)In this thesis, first, joint with Longzhi Lin, we establish estimates for the harmonic map heat flow from the unit circle into a closed manifold, and use it to construct sweepouts with the following good property: each ... 
Selfsimilar solutions to the mean curvature flow in Euclidean and Minkowski space
(Massachusetts Institute of Technology, 2013)In the first part of this thesis, we give a classification of all selfsimilar solutions to the curve shortening flow in the Euclidean plane R² and discuss basic properties of the curves. The problem of finding the curves ... 
Selmer groups as flat cohomology groups
(Massachusetts Institute of Technology, 2014)Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the padic Tate module. In general, the pm1Selmer group Selpmn A need not be determined ... 
Semialgebraic graphs and hypergraphs in incidence geometry
(Massachusetts Institute of Technology, 2019)A (hyper)graph is semialgebraic if its vertices are points in some Euclidean spaces and the (hyper)edge relation is defined by a finite set of polynomial inequalities. Semialgebraic (hyper)graphs have been studied ... 
A semiinfinite cycle construction of Floer homology
(Massachusetts Institute of Technology, 2008)This dissertation is concerned with the foundations of a new approach to Floer theory. As opposed to the traditional approach, which can be viewed as a generalization of Morse theory to an infinite dimensional setting, our ... 
Semiprimary lattices and tableau algorithms
(Massachusetts Institute of Technology, 1995) 
Separable stackel systems
(Massachusetts Institute of Technology, 1947) 
Separation of Laplace's equation
(Massachusetts Institute of Technology, 1948) 
The Severi problem for rational curves on del Pezzo surfaces
(Massachusetts Institute of Technology, 2005)Let X be a smooth projective surface and choose a curve C on X. Let VC be the set of all irreducible divisors on X linearly equivalent to C whose normalization is a rational curve. The Severi problem for rational curves ... 
Shock formation and star formation in galactic spirals,
(Massachusetts Institute of Technology, 1969) 
Shortest paths, Markov chains, matrix scaling and beyond : improved algorithms through the lens of continuous optimization
(Massachusetts Institute of Technology, 2017)In this thesis, we build connections between classic methods from convex optimization and the modern toolkit from the fast Laplacian solver literature, in order to make progress on a number of fundamental algorithmic ...