Browsing Mathematics  Ph.D. / Sc.D. by Title
Now showing items 2140 of 746

Algebraic geometry and representation theory in the Verlinde category
(Massachusetts Institute of Technology, 2019)This thesis studies algebraic geometry and the representation theory of group schemes in the setting of symmetric tensor categories over algebraically closed fields of positive characteristic. A specific focus is paid to ... 
Algorithmic approaches to graph states under the action of local Clifford groups
(Massachusetts Institute of Technology, 2007)Graph states are quantum states (quantum codes) in qndimensional space ... (q being a power of some prime number) which can be described by graphs with edges labeled from the field of order q, Fq. Graph states are determined ... 
Algorithms for genomics and genetics : compressionaccelerated search and admixture analysis
(Massachusetts Institute of Technology, 2013)Rapid advances in nextgeneration sequencing technologies are revolutionizing genomics, with data sets at the scale of thousands of human genomes fast becoming the norm. These technological leaps promise to enable corresponding ... 
Analogues of Kähler geometry on Sasakian manifolds
(Massachusetts Institute of Technology, 2008)A Sasakian manifold S is equipped with a unitlength, Killing vector field ( which generates a onedimensional foliation with a transverse Kihler structure. A differential form a on S is called basic with respect to the ... 
An analysis of network routing and communication latency
(Massachusetts Institute of Technology, 1997) 
Analytic aspects of periodic instantons
(Massachusetts Institute of Technology, 2004)The main result is a computation of the Nahm transform of a SU(2)instanton over R x T³, called spatiallyperiodic instanton. It is a singular monopole over T³, a solution to the Bogomolny equation, whose rank is computed ... 
Analytic surgery and analytic torsion
(Massachusetts Institute of Technology, 1994) 
An analytical theory of moist convection
(Massachusetts Institute of Technology, 1985) 
Analyzing monotone space complexity via the switching network model
(Massachusetts Institute of Technology, 2015)Space complexity is the study of how much space/memory it takes to solve problems. Unfortunately, proving general lower bounds on space complexity is notoriously hard. Thus, we instead consider the restricted case of ... 
Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains
(Massachusetts Institute of Technology, 2016)This thesis consists of two parts. In the first part we count antichains of interval orders and in particular semiorders. We associate a Dyck path to each interval order, and give a formula for the number of antichains of ... 
An application of the Malliavin calculus to infinite dimensional diffusions
(Massachusetts Institute of Technology, 1984) 
Applications and extensions of Fomin's generalization of the RobinsonSchensted correspondence to differential posets
(Massachusetts Institute of Technology, 1991) 
Applications of optimization in probability, finance and revenue management
(Massachusetts Institute of Technology, 1999)The unifying contribution of this thesis is to show that optimization is a very powerful tool that provides unexpected insights and impact on a variety of domains, such as probability, finance and revenue management. The ... 
Applications of probability to partial differential equations and infinite dimensional analysis
(Massachusetts Institute of Technology, 2011)This thesis consists of two parts. The first part applies a probabilistic approach to the study of the WrightFisher equation, an equation which is used to model demographic evolution in the presence of diffusion. The ... 
Applied math in geophysical fluids : partially trapped wave problems and mining plumes
(Massachusetts Institute of Technology, 2018)The first portion of this work focuses on leaky modes in the atmospheric sciences. Leaky modes (related to quasimodes, scattering resonances, and the singularity expansion method) are discrete, oscillatory and decaying ... 
Approximate inference : decomposition methods with applications to networks
(Massachusetts Institute of Technology, 2009)Markov random field (MRF) model provides an elegant probabilistic framework to formulate interdependency between a large number of random variables. In this thesis, we present a new approximation algorithm for computing ... 
Approximating fluid schedules in packetswitched networks
(Massachusetts Institute of Technology, 2004)We consider a problem motivated by the desire to provide exible, ratebased, quality of service guarantees for packets sent over switches and switch networks. Our focus is solving a type of online, traffic scheduling ... 
Approximation algorithms for distributed and selfish agents
(Massachusetts Institute of Technology, 2005)Many realworld systems involve distributed and selfish agents who optimize their own objective function. In these systems, we need to design efficient mechanisms so that systemwide objective is optimized despite agents ... 
Areacontracting maps between rectangles
(Massachusetts Institute of Technology, 2005)In this thesis, I worked on estimating the smallest kdilation of all diffeomorphisms between two ndimensional rectangles R and S. I proved that for many rectangles there are highly nonlinear diffeomorphisms with much ... 
Arithmetic and analytic properties of finite field hypergeometric functions
(Massachusetts Institute of Technology, 2011)The intent of this thesis is to provide a detailed study of the arithmetic and analytic properties of Gaussian (finite field) hypergeometric series. We present expressions for the number of F,points on certain families ...