# Results of REU Research 2016

## REU Mini-Conference held July 18-19, 2016

Schedule and Abstracts

### Participants, Presentations, and Reports

**Algebraic Methods in Mathematical Biology**Mentors: Anne Shiu; Kaitlyn Phillipson, Ola Sobieska, and Robert Williams- Luna Bozeman (Clemson U) and Adriana Morales (U Puerto Rico, Rio Piedras): Analyzing Methods to Determine Pairwise Correlations Between Neuronsslides
- Luna Bozeman (Clemson U) and Adriana Morales (U Puerto Rico, Rio Piedras): No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and diistributive mechnism
- Aaron Chen (Cornell): Neural Codes: Convexity and Computabilityslides
- Jessica Liu (Bard): Groebner Bases and the Neural Idealslides
- Mitchell Eithun (Ripon): Proving Global Stability of Processive Phosphorylation Systemsslides
- Mitchell Eithun (Ripon) and Adriana Morales (U Puerto Rico, Rio Piedras): Stability off Control System of Intracellular Iron Homeostasis: A Mathematical Proofslides

**Algorithmic Algebraic Geometry**Mentors: J. Maurice Rojas; Alperen Ergur, Kaitlyn Hellenbrand, Yuyu Zhu- Kayla S. Cummings (Pomona College): Bounding the Number of Distinct p-adic Valuations of Integer Roots of Certain SPS-Polynomials Slides.
- Erin Lipman (Haverford): Bounding Components in Real Zero Sets of Bivariate Pentanomials Slides.
- Jake Mundo (Swarthmore): Higher-Dimensional Analogues of the Combinatorial Nullstellensatz Slides.
- Cory Saunders (Haverford): Counting the p-adic valuations of the roots of multivariate systems of polynomials Slides.
- Lucy Yang (U Minnesotta): A Complexity Bound for Real Zero Sets of n-variate (n+4)-nomials Slides.

**Number Theory**Mentors: Matt Young, Riad Masri; Adrian Barquero-Sanchez- David Burt (Williams): Moments of L-functions associated to Newforms of Squarefree Level, slides
- Lindsay Cadwallader (U Connecticut): Faltings Heights of CM Elliptic Curves and Special Gamma Values II, slides
- Olivia Cannon (Bowdoin): Faltings Heights of CM Elliptic Curves and Special Gamma Values III, slides
- Tyler Genao (Florida Atlantic U): Faltings Heights of CM Elliptic Curves and Special Gamma Values I, slides
- Samantha Moore (U Northern Colorado): On the Zeroes of Half-Integral Weight Eisenstein Series on Γ
_{0}(4), slides

Algorithmic Algebraic Geometry

Mathematical Modeling in Biology

Number Theory

Everybody