Browsing Mathematics - Ph.D. / Sc.D. by Title
Now showing items 612-631 of 784
-
Sampling-based algorithms for dimension reduction
(Massachusetts Institute of Technology, 2007)Can one compute a low-dimensional representation of any given data by looking only at its small sample, chosen cleverly on the fly? Motivated by the above question, we consider the problem of low-rank matrix approximation: ... -
Scaling limits of random plane partitions and six-vertex models
(Massachusetts Institute of Technology, 2018)We present a collection of results about the scaling limits of several models from integrable probability. Our first result concerns the asymptotic behavior of the bottom slice of a Hall-Littlewood random plane partition. ... -
Scattering theory on compact manifolds with boundary
(Massachusetts Institute of Technology, 1993) -
Scheduling techniques for packet routing, load, balancing and disk scheduling
(Massachusetts Institute of Technology, 1997) -
Schubert calculus in generalized cohomology
(Massachusetts Institute of Technology, 1989) -
Schur Weyl duality in complex rank
(Massachusetts Institute of Technology, 2016)This thesis gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with a distinguished non-zero vector 1) we ... -
Scissors congruence and K-theory
(Massachusetts Institute of Technology, 2012)In this thesis we develop a version of classical scissors congruence theory from the perspective of algebraic K-theory. 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 multi-party protocols under a modern lens
(Massachusetts Institute of Technology, 2013)A secure multi-party 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 Seiberg-Witten equations on a surface times a circle
(Massachusetts Institute of Technology, 2010)In this thesis I study the Seiberg-Witten 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 Seiberg-Witten ... -
The Seiberg-Witten equations on manifolds with boundary
(Massachusetts Institute of Technology, 2011)In this thesis, we undertake an in-depth study of the Seiberg-Witten equations on manifolds with boundary. We divide our study into three parts. In Part One, we study the Seiberg-Witten equations on a compact 3-manifold ... -
Self-shrinkers 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 self-shrinkers. We give a rigidity theorem proving that any self-shrinker ... -
Self-shrinkers 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 ... -
Self-similar 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 self-similar 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 p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined ... -
Semi-algebraic graphs and hypergraphs in incidence geometry
(Massachusetts Institute of Technology, 2019)A (hyper)graph is semi-algebraic if its vertices are points in some Euclidean spaces and the (hyper)edge relation is defined by a finite set of polynomial inequalities. Semi-algebraic (hyper)graphs have been studied ... -
A semi-infinite 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 ... -
Semi-infinite Homology of Floer spaces
(Massachusetts Institute of Technology, 2020)This dissertation presents a framework for defining Floer homology of infinite-dimensional spaces with a functional. This approach is meant to generalize the traditional constructions of Floer homologies which mimic the ...
