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Fall 2021

Jiang, Yangdi

The demand for large dataset and demand of privacy protection are in constantly conflicts as the balance between the two is hard to keep. Differential privacy is a mathematical rigor definition that provides the balance bewteen these two opposite sides. It's developed with the purpose of making...

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...

Fall 2021

Farkhutdinov, Tagir

In this thesis, I developed the ideas of applying the variational method in geometric mechanics to the porous media described as solid elastic materials with embedded ideal (incompressible) fluid, also known as Eulerian fluid. The work includes four chapters and a conclusion. In the Introduction,...

Spring 2021

Wang, Yue

In this thesis, with the purpose of correcting for potential measurement errors in repeatedly-observed matrix-valued surrogates, and examining the underlying association between latent matrix covariates and a binary response, we propose a Bayesian joint model framework. This joint model method...

Fall 2021

Wang, Yibo

A great deal of statistical research has been done in high- and ultrahigh-dimensional settings in recent years. Regularized approaches have been extensively used in dealing with high-dimensional datasets. It is widely acknowledged that robust procedures are important to deal with the influence of...

Fall 2021

Fang, Xi

The Covid pandemic has lasted for over a year influencing everyone's physical and emotional well-beings. Our work is aimed at exploring the capability of various types of functional data clustering methods on the complex Covid data. We collect the Covid data from the Our World in Data website,...

Fall 2021

Agrawal, Nishant

In this thesis, we study the product formula for finitely many multiple Itˆo-Wiener integrals of Levy process, option pricing formula where the stock price is modelled by stochastic delay differential equation (SDDE) driven by Levy process and logarithmic Euler-Maruyama scheme for the SDDE. In...

Fall 2021

O'Brien, Michael John

The theory of convergence structures delivers a promising foundation on which to study general notions of convergence. However, that theory has one striking feature that stands out against all others: it is described using the language of filters. This is contrary to how convergence is used in...

Spring 2021

Lu, Ran

Generalizing wavelets by adding desired redundancy and flexibility, framelets (a.k.a. wavelet frames) are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multi-scale...

Fall 2021

Pak, Andrey

This thesis is dedicated to the study of the general class of random processes, called optional processes, and their various applications in Mathematical Finance, Risk Theory, and Statistics. First, different versions of a comparison theorem and a uniqueness theorem for a general class of...