Showcase of Student Research in Mathematics
Congratulations to all of the participants on a job well done!
In the Spring, the Mathematics Department hosted the 2015 Showcase of Student Research in Mathematics. Taking place over two days, eight participating undergraduate and graduate students gave 20-30 minute presentations on their research projects.
Day One: Tuesday, March 31
Speaker: Ben Anzis (Mathematics undergraduate student)
Title: The Lvov-Kaplansky Conjecture for Lie algebras
Abstract: The Lvov-Kaplansky Conjecture is an incredibly important unproven conjecture regarding the interplay between a specific class of polynomials and matrices. In this talk, we present work done at the Kent State REU in which we prove a low-degree analog of the Lvov-Kaplansky Conjecture for certain classical Lie algebras using linear algebra.
Speaker:Jesse Oldroyd (Mathematics graduate student)
Title: A Brief Overview of Finite Frame Theory
Abstract: Frames have become an important tool in applied harmonic analysis, finding applications in fields ranging from quantum physics to signal processing. This talk will present several fundamental concepts relating to the theory of frames in a finite dimensional Hilbert space and give a short discussion of current problems in the field.
Speakers: Cameron Crandall (Biology undergraduate student) and Anna Rodriguez (Animal and Veterinary Science undergraduate student)
Title: Bacteriophage and lysins: exploring their potential as antibacterial agents using spatial modeling
Abstract: As the levels of antibiotic resistant bacteria continue to grow, new methods of combating bacterial infections need to be developed. Bacteriophages and their lysins provide promising avenues for development of a new antibacterial agent. Using NetLogo, we developed spatial models to simulate the interactions between bacteria, phage, and lysin. Our current research focuses on exploring how phage and their lysins can become effective antibacterial agents for clinical use.
Day Two: Thursday, April 2
Speaker: Masaki Ikeda (Mathematics graduate student)
Title: Introduction to permutation patterns
Abstract: In enumerative combinatorics, the study of permutation patterns blossomed in the 1980s with the Stanley-Wilf conjecture. In this talk, I will introduce the basic concept of permutation patterns, and some approachable examples as well as a brief overview of my doctoral research.
Speaker: Malcolm Rupert (Mathematics graduate student)
Title: An Explicit Theta Lift from Hilbert Modular Forms to Siegel Paramodular Forms
Abstract: Recently N. Freitas, B. V. Le Hung, S. Siksek proved that every elliptic curve defined over a real quadratic number field corresponds uniquely to a Hilbert modular form. Furthermore it was conjectured by A. Brumer and K. Kramer that abelian surfaces defined over the rational numbers correspond to certain Siegel modular forms called paramodular forms. These are both examples of problems in the Langlands program. J. Johnson-Leung and B. Roberts proved the existence of a theta lift which for every Hilbert modular form returns a paramodular form. This talk will discus the strategy for making this theta lift more explicit with the goal of being able to calculate coefficients of paramodular forms. This theta lift provides a way to prove the paramodular conjecture in the specific case of when the abelian surface is the restriction of scalars of an elliptic curve over a real quadratic number field which is not isogenous to its Galois conjugate.
Speaker: Ailene MacPherson (Bioinformatics and Computational Biology graduate student)
Title: Why am I sick?: The mathematics of identifying the genes of disease susceptibility
Abstract: Understanding the genetics of disease susceptibility is one of the fastest growing fields in medical biology. These advances have ushered in the era of personalized medicine, where treatment can now be administered specifically for you and your genome. Discovering the genes that make you susceptible to disease relies heavily on mathematics. In this talk I will introduce you to the underlying mathematics of identifying genes of disease susceptibility, the experimental challenges the field faces, and ultimately why this problem may be much more difficult than we currently realize.Ultimately, I hope to leave you with an appreciation for why a rigorous mathematical understanding of biological experimental methods is essential for their success.
Speaker: Bob Week (Mathematics undergraduate student)
Title: The Mathematics of Coevolution
Abstract: The topic of coevolution is essential to evolutionary theory. However, there is no current method to quantify the strength of coevolution for a given pair of species. Solving this problem would provide key insights to the history of life. This talk will introduce the basics of difference equations, how they have been applied to modeling coevolution, and how such models may provide a path towards finding a solution to the aforementioned problem.