MSP REU: Polynomials & Their Zeros
May 18 - June 18, 2026
The ancient problem on solving polynomial equations (finding roots of polynomials) remains very important in mathematics, and it also has a wide range of applications in many sciences. Polynomial roots display a lot of fascinating behavior and are very easy to plot on a computer and study. In particular, the roots of certain classes of polynomials in the complex plane often display interesting and discernible patterns of distribution that can reveal a lot about the problems from which the polynomials arise.
In this REU, we will explore several projects related to the distribution of roots of polynomials, including:
- Counting real roots of polynomials with real and integer coefficients
- Probabilistic aspects of zero distribution
- Asymptotic distribution of complex zeros near the unit circle and other sets
- Polynomial dynamics and zero distribution
- Heights and norms of polynomials
- Applications of these problems to famous questions in number theory and dynamical systems
This REU is supported by the Mathematical Sciences Program (MSP) of the National Security Agency, and by the Department of Mathematics at Oklahoma State University.
The REU program is excited to recruit 10 students (limited to US citizens) who will be provided with a stipend of $4,000 and paid lodging in the private deluxe suites of Village C, OSU residential housing. Travel for participants from outside of Oklahoma, or from its remote areas, is expected to be covered as well.
All positions have been filled.