Online Shopping and Games, how Algebra Plays a Role
Ellen Ziliak, Ph.D.
Benedictine University
The field of Abstract Algebra is often considered to be a topic in pure mathematics. However, while they are not often included in a standard undergraduate Abstract Algebra class, there are many interesting applications that are very relevant to our current digital society. In this talk I will share some applications that I have studied along with my undergraduate research students. The first set of topics I will discuss have to do with applications to cryptography. While most encryption algorithms currently in use today depend on modular arithmetic, the security of this scheme is based primarily on supposed difficulty of factoring large prime numbers. Since this problem is not provably hard, many algebraists look to see if we can create similar algorithms that rely on other algebraic structures, where the problem has already been shown not to be np hard. We will then transition into how algebra can be used to study other problems. These projects were initially motivated by the use of Grobner Bases to study games like Sudoku, but can lead to applications to many other fields including biology.
Ellen Ziliak is an Associate Professor of mathematics at Benedictine University. Her research interests are in the field of computational group theory. Her current work involves classifying symmetric spaces of the special linear and special orthogonal groups. In addition, she enjoys working with undergraduate students on applied abstract algebra projects, normally in senior capstone projects. Outside of work, she is a mom of four who loves to run. So far she has run 10 half marathons and the Chicago Marathon. She looks forward to running her first in-person race the weekend after this talk.
