Codes, Curves, and Configurations of Points

Algebra and Number Theory Seminar
Event time: 
Tuesday, February 10, 2015 - 11:15am to Monday, February 9, 2015 - 7:00pm
LOM 205
Nathan Kaplan
Speaker affiliation: 
Event description: 

One of the main problems in coding theory is to find large subsets of $(Z/pZ)^n$ such that any two elements differ in at least $d$ coordinates. Some of the best constructions we have come from evaluating each element of a vector space of polynomials at a specified set of points. These include the classical Reed-Solomon and Reed-Muller codes.

We will discuss how interesting codes arise from families of curves over finite fields and how these constructions are related to special configurations of points in projective space. We will see connections to modular forms and to ‘Galois groups of enumerative problems’.