Andrews, Michael Joseph, Ph. D. Massachusetts Institute of Technology(Massachusetts Institute of Technology, 2015)
We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the "dancers to a discordant system." We calculate a Bockstein spectral ...
Donovan, Michael Jack(Massachusetts Institute of Technology, 2015)
In this thesis we study the Bousfield-Kan spectral sequence (BKSS) in the Quillen model category sCom of simplicial commutative FF₂ -algebras. We develop a theory of unstable operations for this BKSS and relate these ...
Glasman, Saul(Massachusetts Institute of Technology, 2015)
This thesis is divided into two chapters. In the first, given symmetric monoidal oc-categories C and D, subject to mild hypotheses on D, we define an oc-categorical analog of the Day convolution symmetric monoidal structure ...
Iriarte Giraldo, Benjamin(Massachusetts Institute of Technology, 2015)
This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertex-set with a totally ordered set, ...
Mendelson, Dana Sydney(Massachusetts Institute of Technology, 2015)
In the first part of this thesis we consider the defocusing nonlinear wave equation of power-type on R3. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In ...