Serving Up Data with Polynomials
Abstract:
Polynomials over finite fields have been employed to protect and transmit information in a variety of ways, starting with Reed-Solomon codes in the 1960s. Reed-Solomon codes are based on polynomials in a single variable and are responsible for the error-correction that powers CDs, DVDs, and QR codes, among many other behind-the-scenes uses. Generalizations included the famous Reed-Muller codes (which inspired polar codes behind 5G) and algebraic geometry codes. The data deluge of the past decade has prompted a new application. In this talk, we consider the use of polynomials and curves over finite fields to share data with multiple groups simultaneously.
Counting and Cyclic Symmetry
Abstract:
Part of combinatorics looks for nice formulas to count various objects. Sometimes these formulas hide an added surprise: when we introduce a variable to turn them into a polynomial, they count the objects with cyclic symmetry, after plugging in a complex root-of-unity for the variable! We will illustrate this with some of our favorite examples, including some that we still find mysterious.
wilkinbs@jmu.edu
540-568-6408
Finance and office matters:
ellis6ja@jmu.edu
540-568-6184
