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.
The deadline for receiving all application materials is April 30, 2026. Please be
sure to apply as soon as possible to receive full consideration, as we will be evaluating
applications on a continual basis until all 10 positions are filled.
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.
The deadline for receiving all application materials is April 30, 2026. Please be
sure to apply as soon as possible to receive full consideration, as we will be evaluating
applications on a continual basis until all 10 positions are filled.