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Fall 2019

Ali, Abid

One of the main difficulties in extending Macdonald’s theory of spherical functions from p-adic Chevalley groups to p-adic Kac-Moody groups is the absence of Haar measure in the infinite dimensional case. Related to this problem is the question of how to generalize the integral defining...

Spring 2020

Su Hwan Kim

This thesis investigates various issues arising from crossover designs, which received great attention for their efficiency. Crossover designs gain advantage over parallel designs for efficient estimation of treatment effects and smaller required sample size as the within-subject variability is...

Spring 2020

Fischer, Samuel

Invasive species and infectious diseases cause significant ecological and economic harm all over the world. Therefore, substantial effort is made across the globe to prevent the spread and decrease the impact of biological invasions and epidemicsby implementing early detection and rapid response...

Fall 2020

Roman Frolov

The main goal of this work is the development of all-speed numerical methods for the compressible Navier-Stokes equations, i.e. methods that remain efficient in incompressible, weakly compressible, and compressible regimes. To achieve this goal we propose algorithms based on the direction...

Spring 2020

Koch, Dean Cameron

The mountain pine beetle (MPB) is among the most destructive eruptive forest pests in North America. A recent increase in the frequency and severity of oubtreaks, combined with an eastward range expansion towards untouched boreal pine forests, has spurred a great interest by government, industry...

Fall 2020

Tatarko, Kateryna

This thesis is devoted to several problems in Random Matrix Theory and Convex Geometry. Its content is based on four papers.

Fall 2020

Davies, Colleen M

Ecological stoichiometry is a framework that allows explicit consideration of nutrient restrictions on growth, and can be used to answer important ecological questions. First, we consider the impact of the turnover rate of producer biomass on ecosystems, since it is usually much faster in aquatic...

Fall 2020

Maher, Robert

The first part of this thesis presents an exposition of some of the links between integrability, matrix models and Airy structures. We first introduce the notion of an integrable hierarchy and a tau function. We then probe tau functions further by considering matrix integrals. These are...

Spring 2020

Shuangming Yang

One popular approach to estimating an unknown function from noisy data is the use of a regularized optimization over a reproducing kernel Hilbert space (RKHS). The solution belongs to a nite-dimensional function space. If we assume the additive measurement noise is Gaussian, then there is a well...

Spring 2020

Contreras, Carlos

Radiation therapy is an important component of cancer treatment. It consists of applying ionizing radiation to kill cells by damaging their DNA and reducing their ability to reproduce and survive. It is reasonable to think that more radiation causes more damage and kills more cells. However, in...