# Results of REU Research 2015

## REU Mini-Conference held July 20-21, 2015

Schedule and Abstracts

### Participants, Presentations, and Reports

**Algebraic Methods in Mathematical Biology**Mentors: Anne Shiu, Jay Walton; Severine Biard, Lauren Grimley, Emma Owusukwaakwaah, Veena Shankaranarayanarao, and Jacob White- Bryan Felix (UT Austin) and Zev Woodstock (James Madison U): An Infinite Family of Chemical Reaction Networks with Multiple Non-Degenerate Equilibria Slides.
- Antoine Marc (Texas A&M): Analysis of an immunological subnetwork, slides.
- Meredith McCormack-Mager (Wellesley College): Testing Thermodynamic Compliance of Chemical Reaction Networks Efficiently, slides
- Diego Lopez (Texas A&M): Incorporating HDL Interaction in an ODE model of Atherosclerosisslides
- Joseph Donnelly (Texas A&M): Synchronizing Molecular Clocks via ATP: What can we predict?slides
- Carlos Munoz (Texas A&M): Report on Testing Thermodynamic Compliance of Chemical Reaction Networks EfficientlySlides on Lyme Disease: A Mathematical Approach
- Caitlin Lienkaemper (Harvey Mudd College): When do neural codes come from convex or good covers?slides

**Algorithmic Algebraic Geometry**Mentors: J. Maurice Rojas; Alperen Ergur, Emma Owusukwaakwaah, and Jacob White- Zander Kelley (Texas A&M): The Number of Roots of Trinomials over Prime Fields, slides.
- Sean Owen (UMBC): Extremal Trinomials over Quadratic Fields, slides .
- Yasmina Marden (Reed College) and Hailey Stierneman (Texas State U, San Marcos): Polynomial System Solving Using Archimedean Tropical Varieties, slides
- Mark Stahl (UT Austin): Refining Fewnomial Theory for Certain 2x2 Systems, slides

**Number Theory**Mentors: Matt Young, Riad Masri; Adrian Barquero-Sanchez- Josiah Banks (Youngstown State University) and Kevin Sheng (Emory University): The Asymptotic Distribution of Andrews' Smallest Parts Function
**(Just accepted for publication in Archiv der Mathematik (Basel)!)**, slides - Polina Vulakh (Bard College) and Sarah Reitzes (Tufts U): Zeros of the Modular Form E
_{k}E_{l}- E_{k+l}, slides

- Josiah Banks (Youngstown State University) and Kevin Sheng (Emory University): The Asymptotic Distribution of Andrews' Smallest Parts Function

Algorithmic Algebraic Geometry | Mathematical Modeling in Biology | Number Theory |