Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996. / Includes bibliographical references (leaves 107-114). / by Serguei Piunikhin. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000. / Includes bibliographical references (p. 197-209) and indexes. / by Peter Sheridan Dodds. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (p. 38). / by Calvin L. Roth. / M.S.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995. / Includes bibliographical references (p. 135-137). / by Wendy Chan. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / On t.p. "n" is subscript. / Includes bibliographical references (p. 61). / by Julia Chislenko. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 107-109). / In this thesis, I prove several results toward constructing a machine that turns Lagrangian correspondences into A[infinity],-functors between Fukaya categories. The core of this construction is pseudoholomorphic quilts with figure eight singularity. In the first part, I propose a blueprint for constructing an algebraic object that binds together the Fukaya categories of many different symplectic manifolds. I call this object the "symplectic A[infinity]-2-category Symp". The key to defining the structure maps of Symp is the figure eight bubble. In the second part, I establish a collection of strip-width-independent elliptic estimates. The key is function spaces which augment the Sobolev norm with another term, so that the norm of a product can be bounded by the product of the norms in a manner which is independent of the strip-width. Next, I prove a removable singularity theorem for the figure eight singularity. Using the Gromov compactness theorem mentioned in the following paragraph, I adapt an argument of Abbas-Hofer to uniformly bound the norm of the gradient of the maps in cylindrical coordinates centered at the singularity. I conclude by proving a "quilted" isoperimetric inequality. In the third part, which is joint with Katrin Wehrheim, I use my collection of estimates to prove a Gromov compactness theorem for quilts with a strip of (possibly non-constant) width shrinking to zero. This features local C[infinity]-convergence away from the points where energy concentrates. At such points, we produce a nonconstant quilted sphere. / by Nathaniel Sandsmark Bottman. / Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Includes bibliographical references (p. 145-151). / We consider a problem motivated by the desire to provide exible, rate-based, quality of service guarantees for packets sent over switches and switch networks. Our focus is solving a type of on-line, traffic scheduling problem, whose input at each time step is a set of desired traffic rates through the switch network. These traffic rates in general cannot be exactly achieved since they treat the incoming data as fluid, that is, they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of switch uses throughout the network in which only whole packets are sent. We prove worst-case bounds on the additional delay and buffer use that result from using such an approximation. These bounds depend on the network topology, the resources available to the scheduler, and the types of fluid policy allowed. / by Michael Aaron Rosenblum. / Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. / Includes bibliographical references (p. 73-74). / For complex reductive Lie algebras g, the classical Harish-Chandra homomorphism allows to link irreducible finite dimensional representations of g to those of certain subalgebras l. The Casselman-Osborne theorem establishes an extension of this link to infinite dimensional irreducible representations. In this paper we present a generalized Harish-Chandra homomorphism construction for Hecke algebras, and establish the corresponding generalized Casselman-Osborne theorem. This homomorphism can be used to link representations of (g, L n K)-pairs to those of (g, L n K)-pairs, where is a certain subalgebra of g as in the classical case. Since representations of such pairs are closely related to those of the underlying Lie group G, this construction is a good first approximation to lifting the Harish-Chandra homomorphism from the Lie algebra to the Lie group level. / by Karen Bernhardt. / S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997. / Includes bibliographical references (leaves 60-62). / by Colin Ingalls. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1939. / Vita. / Includes bibliographical references (leaves 47-50). / by Martha Hathaway Plass. / Ph.D.