Browsing Department of Mathematics by Title
Now showing items 648667 of 826

Samplingbased algorithms for dimension reduction
(Massachusetts Institute of Technology, 2007)Can one compute a lowdimensional 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 lowrank matrix approximation: ... 
Scaling limits of random plane partitions and sixvertex 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 HallLittlewood 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 SchurWeyl duality in the setting of Deligne categories. Given a finitedimensional unital vector space V (i.e. a vector space V with a distinguished nonzero vector 1) we ... 
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 ...