# Alumni Dissertations

• ### Groups, Complexity, Cryptology

Author:
Maggie Habeeb
Year of Dissertation:
2012
Program:
Mathematics
Delaram Kahrobaei
Abstract:

The field of non-commutative group based cryptography has flourished in the past twelve years with the increasing need for secure public key cryptographic protocols. This has led to an active line of research called non-abelian group based cryptography.

• ### Derived noncommutative deformation theory

Author:
Joseph Hirsh
Year of Dissertation:
2013
Program:
Mathematics
John Terilla
Abstract:

We define derived deformation theory with parameters over an operad $O$, and prove that the $\infty$-category of such theories is equivalent to the $\infty$-category of $O^{!}$-algebras.

• ### Length spectrum metric and modified length spectrum metric on Teichmüller spaces

Author:
Francisco Jimenez Lopez
Year of Dissertation:
2013
Program:
Mathematics
Jun Hu
Abstract:

The length spectrum function defines a

• ### On the rank of 2-primary part of Selmer group of certain elliptic curves

Author:
KWANG HYUN KIM
Year of Dissertation:
2012
Program:
Mathematics
Victor Kolyvagin
Abstract:

Kolyvagin proved very remarkable results on Mordell-Weil groups and

Author:
Terence Kivran-Swaine
Year of Dissertation:
2011
Program:
Mathematics
Carlos Moreno
Abstract:

The admissible dual of SL2(Q2) is constructed uniformly, based on a method adapted from the the theory of cuspidal types of GL2(F).

• ### On critical poins for Gaussian vectors with infinitely divisible squares

Author:
Hana Kogan
Year of Dissertation:
2009
Program:
Mathematics
Michael Marcus
Abstract:

This paper is concerned with necessary conditions for infinite divisibility of the Gaussian squares with non-zero means. A Gaussian vector G with zero mean is said to have a critical point α, such that 0≤α≤∞

• ### Non-commutative cryptography: Diffie-Hellman and CCA secure cryptosystems using matrices over group rings and digital signatures

Author:
Charalambos Koupparis
Year of Dissertation:
2012
Program:
Mathematics
Delaram Kahrobaei
Abstract:

As computing speed has been following Moore's law without any inclination of tapering out, the need for ever more secure cryptographic protocols is becoming more and more relevant. During the past one and a half decades the field of non-commutative (or on-abelian) group based cryptography has seen a surge in interest.

• ### Smooth Convergence Away From Singular Sets and Intrinsic Flat Continuity of Ricci Flow

Author:
Year of Dissertation:
2013
Program:
Mathematics
Chrisitina Sormani
Abstract:

In this thesis we provide a framework for studying the smooth limits of Riemannian metrics away from singular sets. We also provide applications to the non-degenrate neckpinch singularities in Ricci flow. We prove that if a family of metrics, $g_i$, on a compact Riemannian

• ### The Geometry of Lattice-Gauge-Orbit Space

Author:
Michael Laufer
Year of Dissertation:
2011
Program:
Mathematics
Peter Orland
Abstract:

In this paper, the Riemannian geometry of gauge-orbit space on the lattice with open boundary conditions is explored. It is shown how the metric and inverse metric tensors can be calculated, and further how the Ricci curvature might be calculated. The metric tensor and the inverse metric tensor are calculated for special cases, and some conjectures about the curvature of the space are made, which, if true, would move towards implying a mass gap in the theory.

• ### Resplendent models generated by indiscernibles

Author:
Whanki Lee
Year of Dissertation:
2013
Program:
Mathematics
Roman Kossak
Abstract:

In this thesis I study the question: Which first-order structures are generated by indiscernibles? J. Schmerl showed that if L<\italic> is a finite language, every countable recursively saturated L<\italic>-structure in which a form of coding of finite functions is available is generated by indiscernibles. Further, he showed that such a structure has arbitrarily large extensions which are generated by a set of indiscernibles, resplendent, and L<\italic>_{&infin,&omega}-equivalent to the original structure. Proofs of these theorems are complex and use a combinatorial lemma whose proof in Schmerl's paper has an acknowledged gap. I offer a complete proof of a more direct combinatorial lemma from which Schmerl's theorems follow.