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### An Introduction to Bernstein-Gel’fand-Gel’fand Correspondence

(2022-08-04)

This master's thesis serves as an introduction to the Bernstein-Gel'fand-Gel'fand correspondence first written in 1978. We shall cover some of the fundamental objects that the reader may not be familiar with, mainly tensor ...

### Color Trades on Graphs

(2022-08-03)

Edge-colorings of graphs have a rich history and are widely studied. Trade spectra of
graphs are relatively new and ripe for study. The color-trade-spectrum of a graph G is defined
to be the set of all t for which there ...

### Solvability and exact moment asymptotics for the interpolated stochastic heat and wave equation and the existence of an invariant measure for a special case.

(2022-08-05)

This thesis will consist of two main projects, Chapters 2 and 4, and a smaller project in Chapter 3. We will be studying a general space-time fractional stochastic partial differential equation in Chapters 2 and 3 and the ...

### Parabolic-Elliptic Chemotaxis Models with Singular Sensitivity

(2022-07-25)

Chemotaxis describes the movement of biological cells or organisms in response to certain chemicals in their environments and occupies an essential role in coordinating cell movement in many biological circumstances such ...

### The Slow-Coloring Game on Path Power Graphs

(2022-11-16)

The Slow-Coloring Game is a game played on a graph G by two players which we will refer to as Lister and Painter. In the ith round, Lister marks a nonempty subset M of V (G) of uncolored vertices as eligible to receive ...

### Statistical Inference for High-Dimensional Regularized Huber Regression

(2023-04-18)

With the rapid advancement of technology, the amount of available data for extracting interesting insights and meaningful patterns has grown exponentially, resulting in a significant increase in the dimensionality of ...

### Existence of L_d(n) and ML_d(n,k)

(2023-04-28)

We are given an n x n array, ML(n,k), with integers n, d, k > 0 such that n=mk and each symbol in {0, ..., m-1} appears in each row and column of the ML(n,k) exactly k times. We aim to construct an ML_d(n,k) with the ...

### Embedding and Coloring Designs

(2023-05-04)

This dissertation focuses on two problems in design theory. Techniques from graph theory are frequently utilized and therefore the proofs may also be of interest to graph theorists.
The first problem focuses on ...

### Forbidding Monchromatic and Rainbow Cycles and Families of Cycles

(2023-05-01)

In this dissertation, we avoid certain cycles and families of cycles in complete graphs. Introduced by Axenovich and Choi \cite{2011NoteMonotonicity}, the mixed Ramsey spectrum, $\mrs{F}{H}$,
is the set of numbers $k$ ...

### Probability Equivalent Level of Value at Risk and Expected Shortfall

(2023-05-02)

Probability Equivalent Level of Value at Risk and Expected Shortfall (PELVE) is a novel risk measure proposed and explored by Li and Wang (2020), in [16]. It is motivated by the transition from 99% Value-at-Risk (VaR) to ...