Research Training Group in Coding Theory, Cryptography, and Number Theory Hosts Summer Programs

August 25, 2017

Clemson’s NSF-funded Research Training Group (RTG) in Coding Theory, Cryptography, and Number Theory hosted three programs in Summer 2017:
pREU (preliminary Research Experience for Undergraduates) , REU, and PaRR (Path to Research Readiness).

The pREU focused on coding for distributed storage. A team of five undergraduates, Lia Bozzone (Vassar College), Sam Ditkovsky (Haverford College), Emma Lee Fancher (University of North Alabama), Jennifer Johannes (SUNY Brockport), and Egwuchukwu Kalu (Florida State University) was led by Gretchen Matthews and assisted by recent PhD graduate Fiona Knoll. During the 5-week program, students studied finite fields, curves, and other algebraic structures, and applied this knowledge to generalize and improve an error-correction algorithm for large families of algebraic geometry codes for use in distributed storage systems.

The 8-week REU in Coding Theory and Number Theory hosted 8 supported participants along with one self-supported international student from Nepal. These students worked in groups of 3 and focused problems related to elliptic curves, batch properties of Hamming and Reed-Müller codes and the multicast triangular semi-lattice network. Graduate students Travis Baumbaugh and Huixi Li served as mentors. This work has resulted in 3 research papers which will be submitted for publication in the near future along with an additional paper still in preparation. The students by group are as follows.
Project 1: Distribution on Primes and Elliptic Curves.
– Antony Angwu (University of Maryland Baltimore County)
– Phillip Harris (University of Illinois at Urbana-Champaign)
– Siddarth Kannan (Pomona College)
Project 2: Batch Properties of Hamming and Reed-Müller Codes
– Yariana Diaz (Amherst College)
– Sophia Friesenhahn (Willamette University)
– Alexander Vetter (Villanova University)
Project 3: Multicast Triangular Semilattice Network
– Angelina Grosso (University of Kentucky)
– Shiwani Varal (The College of Wooster)
– Emily Zhu (Carnegie Mellon University)

PaRR (Path to Research Readiness) is a summer program designed for incoming and first year students interested in coding theory, cryptography, or number theory. The goal is to introduce students to concepts they normally would not encounter until later in graduate school; this exposes them to topics that allow them to make a more informed choice of research area. A secondary purpose of the program is to expose students to topics essential for research in these areas that are not covered in first year courses at Clemson. This summer there were five students that participated in PaRR; three were incoming students and two were students that just completed their first year. Topics covered in this PaRR were basic coding theory, introductory algebraic geometry, elliptic curves, algebraic geometry codes, and point-set topology.

To learn more about the RTG in Coding Theory, Cryptography, and Number Theory, please see https://www.math.clemson.edu/ccnt/.