Search

Fall 2012

Kroll, Jeffrey P

This thesis is interested in the topological recursion first introduced in \cite{CEO} and generalized to algebraic curves in \cite{Eynard:2007,Eynard:2008}. A presentation of the Hermitian matrix model is given and includes a derivation of this topological recursion. The second part introduces a...

Fall 2021

Patterson, Devin C.D.

Topological Recursion began its life as a series of recursive equations aimed at solving constraints which occur in matrix models of Quantum Field Theory. After its inception, Topological Recursion was given a more abstract formulation in terms of Quantum Airy Structures and has since been of...

Spring 2017

Dauphinee, Tyler LJ

We explore the connection between Eynard-Orantin Topological Recursion (EOTR) and the asymptotic solutions to differential equations constructed with the WKB method (named for its creators Wentzel, Kramers and Brillouin). Using the Airy spectral curve as an initial example, we propose a general...

Fall 2015

Huang, Qianhong

Let a locally compact semitopological semigroup S have a separately con- tinuous left action on a locally compact Hausdorff X. We define a jointly continuous left action of the measure algebra M(S) on the bounded Borel measure space M(X) which is an analogue of the convolution of measure alge-...

Fall 2014

Petrov, Pavel

Persistent Homology broadly refers to tracking the topological features of a geometric object. This study aims to use persistent homology to explore the effect of Human Biotherapy on patients suffering from Clotridium Difficile Infection. The data is presented in the form of several distance...

Fall 2017

Zhang, Ning

In this thesis, some topics in convex geometric analysis and discrete tomography are studied. Firstly, let K be a convex body in the n-dimensional Euclidean space. Is K uniquely determined by its sections? There are classical results that explain what happens in the case of sections passing...

Fall 2017

Morrill, Ryan W

In this thesis, we formulate and prove the theorem of quadratic reciprocity for an arbitrary number field. We follow Hecke and base our argument on analytic techniques and especially on an identity of theta functions called theta inversion. From this inversion formula and a limiting argument, we...

Fall 2013

Rahmati, Saeed

This thesis has two parts. In the first part we start from an arbitrary exact couple of R-modules and describe completely how the E-infinity terms of the associated spectral sequence relate to adjacent filtration stages of the universal (co-)augmenting objects of the exact couple. This advances...

2003

Cao, Guangjun

Fall 2018

Tao, Sile

This thesis studies mixture models, in particular the estimation of mixing distributions and their applications to empirical Bayes prediction. The objectives are two-fold: to study the large-sample property of empirical Bayes estimators; to develop algorithms for the nonparametric estimation of...