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Spring 2011

Tuncer, Serhan

In 1990 James D. Lewis made a conjecture on the representability of algebraic Chow groups of projective algebraic manifolds. We prove that his conjecture holds for smooth complex complete intersections satisfying a numerical condition and consider some applications to motives.

Fall 2013

Yu, Dengdeng

This thesis deals with the problem proposed by Ye and Zhou (2007): Is a Q-optimal minimax design still symmetric if the requirement of $\int_\chi xm(x)dx = 0$ is removed? We have shown that for the simple linear regression, considering only the variance, a Q-optimal minimax design is necessarily...

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 2016

Ye, Wenrui

The thesis consists of two closely related parts: (i) Cesaro summability of the spherical h-harmonic expansions on the unit sphere, and (ii) Bochner-Riesz summability of the inverse Dunkl transforms on d-dimensional real space, both being studied with respect to the weight that is invariant under...

Spring 2012

Samuylova, Evgenia

The topic of the thesis is an overview of some sequential and change-point detection methods with applications to clinical trials. Performing sequential monitoring is important for ethical, economical and other reasons. It is important to terminate a study as soon as possible when potentially...

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...

Fall 2018

Joshi, Aniket

Vector-valued modular forms of the Weil representation are an indispensable tool in diverse areas of mathematics such as enumerative geometry of Calabi-Yau manifolds and rational conformal field theory. In this thesis, we study Hecke operators on vector-valued modular forms of the Weil...

Fall 2015

Sadeghi,Samira

Classical time-series theories are mainly concerned with the statistical analysis of light-tailed and short-range dependent stationary linear processes. Applications in network theory and financial mathematics lead us to consider time series models with heavy tails and long memory. Heavy-tailed...

Fall 2016

O'Brien, Michael J

In this thesis we describe basic properties of unbounded norm convergence (un-convergence) and investigate its relationship with other convergences in Banach lattices. In particular, we show that in order continuous Banach lattices with a weak unit, un-convergence can be viewed as a...

Spring 2016

Du,Peng

The global dynamics of complex systems is investigated in this thesis, using the framework of coupled dynamical systems. For a coupled dynamical system on an interaction network, we show the impact of the connectivity of the interaction network on its dynamical behavior. We lay particular...