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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...

Fall 2013

Kostiuk, Jordan Allan

Heegner points on modular curves play a key role in the solution of Hilbert’s twelfth problem for qua- dratic imaginary fields, as well as the proof of the Birch and Swinnerton-Dyer conjecture for the case ords=1 L(E, s) ≤ 1. The relationship between Heegner points and Hilbert’s twelfth is...

Fall 2014

Yahorau, Uladzimir

Chevalley's theorem on the conjugacy of split Cartan subalgebras is one of the cornerstones of the theory of simple finite dimensional Lie algebras over a field of characteristic 0. Indeed, this theorem affords the most elegant proof that the root system is an invariant of the Lie algebra. The...

Spring 2020

Loliencar, Prachi

Abstract harmonic analysis is well established on compact Hausdorff admissible right topological (CHART) groups. Specifically these groups are one-sided analogues of topological groups, where the elements that multiply continuously on the other side are dense in the group. The analytic theory of...

Fall 2016

Frolova, Nadezda

There is an increasing interest in extreme value analysis for financial and climate data. Various statistical methods have been developed for estimating extreme value dependence in time series data sets and the field continues to grow. In this work we consider four statistical methods for...

Fall 2010

Wang, Xupeng

In financial market, risk management is very critical to a company. However, some risks in the market ( market risk) can not be controlled or eliminated through management improvement or appropriate asset allocation. Thus, it is important to accurately measure these kinds of risks. In this...

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...

Fall 2016

Salame, Khadime

In this thesis we are interested in fixed point properties of representations of semi-topological semigroups of non-expansive mappings on weak and weak* compact convex sets in Banach or dual spaces. More particularly, we study the following problems : Problem 1 : Let F be any commuting family of...