Planned maintenance alert  Monday, April 21: DSpace@MIT will undergo maintenance activities that will affect service availability and access to file content. While the service interruptions should be brief, access to file content may take longer to restore. Status updates will be posted to http://3down.mit.edu/.
Browsing Theses  Mathematics by Issue Date

Horel, Geoffroy (Geoffroy Jean)
(Massachusetts Institute of Technology, 2013)
In this thesis, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad [epsilon]d of little ddimensional disks, we show ...

Ullman, John Richard
(Massachusetts Institute of Technology, 2013)
In this thesis, we analyze a variant of the slice spectral sequence of [HHR (or SSS) called the regular slice spectral sequence (or RSSS). This latter spectral sequence is defined using only the regular slice cells. We ...

Loh, PoRu
(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 ...

Halldórsson, Höskuldur Pétur
(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 ...

Marberg, Eric (Eric Paul)
(Massachusetts Institute of Technology, 2013)
This thesis considers three topics related to the representations of Coxeter systems, their Hecke algebras, and related groups. The first topic concerns the construction of generalized involution models, as defined by Bump ...

Suh, Uhi Rinn
(Massachusetts Institute of Technology, 2013)
The first part of the thesis provides three equivalent definitions of a classical finite Walgebra Wfin(g, f) and two equivalent definitions of a classical affine Walgebra W(g, f, k) associated to a Lie algebra g, a ...

Haugseng, Rune
(Massachusetts Institute of Technology, 2013)
The goal of this thesis is to begin to lay the foundations for a theory of enriched [infinity]categories. We introduce a definition of such objects, based on a nonsymmetric version of Lurie's theory of [infinity]operads. ...

Li, Nan, Ph. D. Massachusetts Institute of Technology
(Massachusetts Institute of Technology, 2013)
We studies two examples of polytope slices, hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart ...

Chiu, Jiawei
(Massachusetts Institute of Technology, 2013)
In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...

Clausen, Dustin (Dustin Tate)
(Massachusetts Institute of Technology, 2013)
Let X be a regular arithmetic curve or point (meaning a regular separated scheme of finite type over Z which is connected and of Krull dimension </= 1). We define a compactlysupported variant Kc(X) of the algebraic Ktheory ...

Levin, Alex, Ph. D. (Alexander). Massachusetts Institute of Technology
(Massachusetts Institute of Technology, 2013)
In this thesis, we present several algorithmic results for problems in spectral graph theory and computational biology. The first part concerns the problem of spectral sparsification. It is known that every dense graph can ...

Liang, Xiangdong, Ph. D. Massachusetts Institute of Technology
(Massachusetts Institute of Technology, 2013)
Capillary instability (PlateauRayleigh instability) has been playing an important role in experimental work such as multimaterial fiber drawing and multilayer particle fabrication. Motivated by complex multifluid geometries ...

Molác̆ek, Jan, Ph. D. Massachusetts Institute of Technology
(Massachusetts Institute of Technology, 2013)
Coalescence of a liquid drop with a liquid bath can be prevented by vibration of the bath. In a certain parameter regime, a purely vertical bouncing motion may ensue. In another, this bouncing state is destabilized by the ...

Singh, Bhairav
(Massachusetts Institute of Technology, 2013)
One of the fundamental results in geometric representation theory is the geometric Satake equivalence, between the category of spherical perverse sheaves on the affine Grassmannian of a reductive group G and the category ...

Boyle, Elette Chantae
(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 ...

Fortuna, Giorgia
(Massachusetts Institute of Technology, 2013)
This thesis mainly deals with the study of the category of admissible modules for the affine KacMoody algebra at the critical level, and the study of its center.

Khandhawit, Tirasan
(Massachusetts Institute of Technology, 2013)
In this thesis, we extend Manolescus and KronheimerManolescus construction of Floer homotopy type to general 3manifolds. This Floer homotopy type is a candidate for an object whose suitable homology groups recover Floer ...

Pereira, Luis Alexandre Meira Fernandes Alves
(Massachusetts Institute of Technology, 2013)
The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that ...

Zhang, Yan, Ph. D. Massachusetts Institute of Technology
(Massachusetts Institute of Technology, 2013)
Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory ...

Yun, Taedong
(Massachusetts Institute of Technology, 2013)
We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by Fomin GreeneReinerShimozono, and we extend this notion to ...