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Fall 2018

Auger, Jean

This thesis is about the theory of vertex operator algebras and their representations. Its main results provide new examples of logarithmic C2-cofinite vertex operator algebras. These include closure of the characters under modular transformations with explicit determination of the modular...

Fall 2018

Kostiuk, Jordan

The formalism of variations of local systems is applied in a geometric setting to define a notion of geometric variation of local systems; this provides a natural framework with which to study families of fibrations of Kahler manifolds. We apply this formalism in various contexts, starting with...

Fall 2019

Mitra, Joshua

The problem of benchmarking in financial markets is an important one. It could be a mutual fund looking to meet its cash inflows and outflows or a brokerage that has been contracted a benchmark price. There is also often incentive to manipulate benchmark. We introduce a discrete-time market model...

Spring 2012

Lukyanova, Anastasia

Spatial heterogeneity is an important characteristic of large-scale composting, however, only a few spatial models for composting exist to date. In this thesis, a novel spatial model for composting is developed. The model is applicable for any one-, two-, or three-dimensional pile geometry. It...

Spring 2012

Wanye, Randy Kanyiri

In this thesis, we will study singular solutions of the Kadomtsev-Petviashvili equation (ut+6uux+uxxx)x+3α^2 u_yy=0, α^2=±1 that will help improve our understanding and if possible give indicators to the occurrence of rogue waves. We will only study the nonlinear interaction of two such...

Fall 2018

Guo, Hongyan

This thesis gives two realizations of fgc extended affine Lie algebras, as fixed point subalgebras and as descended objects. Fgc stands for “finitely generated over the centroid ” . All extended affine Lie algebras are fgc except for a well understood family of type A. In the process, the Lie...

Fall 2019

Mackall, Eoin

This thesis investigates the Chow ring, and neighboring functors, of a Severi-Brauer variety. The approach taken here heavily depends on the computation of lower K-groups of a Severi-Brauer variety.We construct a functor (for an arbitrary scheme essentially of finite type over a field) that is a...

Fall 2020

Chidambaram, Nitin Kumar

In this thesis, we study some aspects of algebraic geometry that have had a significant influx of ideas from physics. The first part focuses on the Eynard- Orantin topological recursion and its variants as a theory of enumerative ge- ometry. We investigate the conjectural relationship between the...

Fall 2015

Riveros Pacheco, David Ricardo

For K/k a finite Galois extension of number fields with G=Gal(K/k) and S a finite G-stable set of primes of K which is "large", Gruenberg and Weiss proved that the ZG-module structure of the S-units of K is completely determined up to stable isomorphism by: its torsion submodule, the set S, a...

Fall 2019

Marculis, Nathan

Integrodifference equations are a common tool used in ecology to model the spread of populations. In this thesis, I explore the neutral genetic patterns formed by range expansions and how dispersal-reproduction trade-offs impact the spread of populations. In Chapter 2, we investigate the inside...