# Results of REU Research 2019

## REU Mini-Conference, July 22-23, 2019

Schedule and Abstracts

### Participants, Presentations, and Reports

**Algorithmic Algebraic Geometry**Mentors: Prof. J. Maurice Rojas; Joann Coronado- Lauren Gernes (Lewis University): Probability of Easily Approximating the Positive Real Roots of Trinomials (Part 1), slides, report (joint with Laurel Newman)
- Laurel Newman (Harvey Mudd College): Probability of Easily Approximating the Positive Real Roots of Trinomials (Part 2), slides
- Tyler Feemster (Princeton University): On the Existence and Number of Roots of Polynomials over Prime Fields, slides, report
- Caleb Robelle (University of Maryland, Baltimore County): Counting Points on Arbitrary Curves Over Prime Power Rings, slides, report

**Algebraic Methods in Mathematical Biology**Mentors: Prof. Anne Shiu; Nida Obatake and Thomas Yahl- Seth Gerberding (University of South Dakota): Preserving Identifiability: Removing Leaks, Moving Outputs, and a New Model, slides, report
- Brianna Gambacini (University of Connecticut): Neural codes (Part 1), slides, report (joint with Sam Macdonald)
- Sam Macdonald (Willamette University): Neural codes (Part 2), slides, report (joint with Brianna Gambacini)
- Dilruba Sofia (University of Massachusetts, Dartmouth): An Efficient Way of Understanding the Maximum Number of Steady States of Chemical Reaction Networks, slides, report

**Number Theory**Mentors: Prof. Matt Young and Prof. Riad Masri; Wei-Lun Tsai- Stephanie Gaston (CSU Dominguez Hills): An average of generalized Dedekind sums (Part 1), slides, report (joint with Travis Dillon)
- Travis Dillon (Lawrence University): An average of generalized Dedekind sums (Part 2), slides, report (joint with Stephanie Gaston)
- Asimina Hamakiotes (Macaulay Honors at Baruch College): Asymptotic Distribution of the Partition Crank (Part 1), slides, report (joint with Aaron Kriegman)
- Aaron Kriegman (Haverford College): Asymptotic Distribution of the Partition Crank (Part 2), slides

Algorithmic Algebraic Geometry

Algebraic Methods in Mathematical Biology

Number Theory