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1 Youatt, Catherine C.Mathematics in Visual Art and BalletCultures all over the globe utilize both mathematics and ballet to understand the world and to express their distinct realities. In this way, mathematics and art interact, both with math creating new visual art fields, like fractal artworks, and with art influencing mathematics, as with Renaissance ...2019
2 Tse, JustinThe Linear Algebra of the Last Passage Percolation ModelWe study the linear algebra of the last passage percolation model. In this model, we want to find the statistics of maximal paths through a randomly weighted grid. Specifically we focus on bases of the set of path lengths made from paths. The maximum path length is a deterministic function of a much...2017
3 Johnson, DylanModular forms, Elliptic Curves, and Their Connection to Fermat's Last TheoremFermat's Last Theorem (FLT) states that if n is an integer greater than three, the equation xn + yn = zn has no integer solutions with xyz 6= 0. This incredible statement eluded proof for over three-hundred years: in that time, mathematicians developed numerous tools which finally proved FLT in 1995...2020
4 Bull, August JohnStudying Galois Representations Using Elliptic CurvesDiophantine equations and their solution sets are prominent subjects of study in number theory. These equations are often studied modulo prime numbers or prime ideals in field extensions. Galois Theory is well-suited to study field extensions, but Galois groups are often mysterious. To remedy this, ...2020
5 Allam, JeremyLow-energy satellite transfer from Earth to MarsA new type of satellite transfer that uses half the amount of fuel as conventional transfers has been discovered. This transfer, called a low-energy transfer, proved to work in 1991 when a Japanese satellite successfully went in orbit around the moon using this technique. Since then, more research h...Space vehicles -- Dynamics -- Mathematics Space flight to Mars -- Mathematics2015-04
6 Du, WantongThe role of mRNA decay in a genetic switchGenes can be switched on or off by regulatory proteins. For example, two genes may each synthesize a protein that downregulates the other gene, creating a repressor- repressor switch that has two stable steady states: one being when the first gene is "on" and the second gene is repressed, and the ot...Messenger RNA - Research; Genetic regulation - Research; Genetic switch; Gene repression; Neural circuitry2016-04
7 Tuft, MarieQuantitative analysis of virus trafficking in a biological cellVirus replication is a complex process that is important to understand. If a virus is to successfully infect a host cell it must travel from the cell wall to the nucleus by hijacking that cell's existing transport system of microtubules. This motion occurs as two iterated steps: passive diffusion th...Viruses -- Reproduction -- Mathematical models; Virus trafficking2015-05
8 Bingham, KouverReflection groups and coxeter groupsIn this paper we give a survey of the theory of Coxeter Groups and Reflection groups. This survey will give an undergraduate reader a full picture of Coxeter Group theory, and will lean slightly heavily on the side of showing examples, although the course of discussion will be based on theory. We'll...Finite groups2014-07
9 Thomas, J PaytonStability of genetic oscillators with distributed delayed feedbackGenetic oscillators govern periodic phenomena in biology including circadian rhythms and are also the basis of biological clocks used in the design of synthetic genetic circuits. Models of genetic oscillators tend to neglect biological detail, however, because biological systems tend to be too compl...2023
10 Ellingson, DrewBitangent lines to planar quartic curves in algebraic and tropical geometryBitangents are lines which are tangent to a curve at two points. The bitangents of a classical quartic are well understood, and a result originally due to Cayley tells us that there are always precisely 28 bitangents to a generic quartic plane curve. When looking at Tropical Geometry, the situation ...Tropical geometry; Curves, Quartic; Curves, Algebraic; Bitangents2015-04
11 Zhao, MichaelBinary Hermitian Forms and Optimal EmbeddingsLet L=K be a quadratic extension of global fields, and OL the ring of integers of L. We prove two correspondences between (i) binary L-hermitian forms which represent 1 and optimal embeddings of L into a quaternion algebra, (ii) integral binary OL-hermitian forms which represent 1 and embeddings of ...2017
12 Baker, JustinDesigned Swarming Behavior Using Optimal Transportation NewworksModels of swarming behavior aid in disaster planning, direct the actions of ware- house robots, and can map the foraging characteristics of insects. These mod- els use the optimal behavior of individual agents to determine the behavior of the larger population. Optimal transportation is one such mod...2019
13 Zheng, KennethDyck Paths and Random TreesWe give an expository survey of random trees, focusing on the interplay between plane trees and Dyck paths. The material explained here summarizes what can be found in Aldous [1], Le Gall [10], and Drmota [6]. The bijection between plane trees and Dyck paths serves as motivation for the connection b...2017
14 Tang, AnnaMathematical model of drug resistance in ER+ breast Cancer: the role of the microenvironmentOne of the main obstacles to treating cancer is its ability to evolve and resist treatment. In this project, we are primarily interested mathematically modeling how the cancer microenvironment interacts with cancer cells and affects cancer's response to therapy. We aim to develop the mathematical mo...2023
15 Halberg, CharlesOn causality in machine learningAlthough the studies of causal inference and machine learning arose independently, there are emerging intersections which are proving fruitful for both fields. One of the major modern challenges in AI is to develop robust, generalizable models which can perform across a number of different tasks wit...2022
16 Bowen, BradyFractal geometry of melt ponds: Modeling the fractal geometry of arctic melt ponds using the level sets of random surfacesDuring the late spring, most of the Arctic Ocean is covered by sea ice with a layer of snow on top. As the snow and sea ice begin to melt, water collects on the surface to form melt ponds. As melting progresses, sparse, disconnected ponds coalesce to form complex, self-similar structures which are c...Melt pond geometry2016-04
17 Wang, WenyiImaging in a homogeneous aluminum plate by using ultrasonic wavesThis project is about detecting and imaging damage (such as cracks) in a plate by using ultrasonic waves. The waves are generated by a source (an ultrasonic transducer) that is part of a robot that can move on the plate. The waves traveling in the plate are recorded at a receiver (another ultrasonic...Ultrasonic transducer - Mathematics; Kirchoff migration - Research2014-12
18 Beams, AlexanderImplications of antibiotic use for co-infections when a fitness trade-off for resistance is presentHow much does indiscriminate antibiotic use promote the spread of antibiotic-resistant infections in a population? Assuming a fitness trade-off for resistance exists, it is possible for an antibiotic-vulnerable strain to outlast a resistant type within an untreated host carrying both. That means pru...Drug resistance in microorganisms -- Mathematical models Co-infections2015
19 Copinga, AidanOptimal transport and applications in partial differential equationsIn the 18th century, Gaspard Monge created a mathematical framework to find the best way to describe the optimal way to rearrange the dirt dug out from the land into castle walls or other desired shapes. More recently, in the 20th century, Leonid Kantorovich explored infinite dimensional optimizatio...2022
20 Gondolo, AlessandroCharacterization and Synthesis of Rayleigh Damped Elastodynamic NetworksWe consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (Rayleigh damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such netw...Damping (Mechanics) - Mathematics2013-05
21 Scott, IsabelleTropical analog to the log canonical thresholdIn algebraic geometry, the log canonical threshold is a property of singularities of planar curves. While singularities have multiplicities, the log canonical threshold can be a more telling invariant. It helps to classify curves beyond what the multiplicity indicates by examining how quickly the in...Geometry, Algebraic2013-04
22 Kroll, TylerNumerical floating-point code: precision-independence, base-independence, and other programming considerationsThe knowledge and skills of the floating-point-literate mathematician are seldom lauded, though central to the art of translating the world of mathematics into the language of computers. This thesis highlights the importance of floatingpoint literacy through various high-utility techniques relevant ...2020
23 Fischer, PaulHigh-Performance Computing Performance Metric AnalysisAt present, a signi#12;cant amount of ongoing scienti#12;c research relies on computational models. High-performance computing (HPC) resources are often required to obtain results in a reasonable amount of time. However, as physical and practical limitations constrain the performance progression of ...2019
24 McDaniel, TylerUtah's Pathways to Higher Education: a Critical, Quantitative AnalysisThis work uses linear and nonlinear models in order to predict student success and pathways in higher education in the state of Utah. Postsecondary Grade Point Average is used as a metric for success in higher education. Pathways are identified using clustering analyses, which group observations a...Higher education and state - Utah; Higher education and state - United States; Low-income students - United States
25 Sullivan, Steven M.A trace formula for G2An n-dimensional matrix representation of a group G on a vector space V is a homomorphism from G to GL(V). For our purposes, we consider an irreducible representation to be a representation which cannot be decomposed into the direct sum of smaller-dimensional representations. Let H be a subgroup of ...Trace formulas2013-05
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