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Colloquium in Honor of Hispanic Heritage Month – Ivelisse Rubio, University of Puerto Rico
October 8 @ 11:00 am - 12:00 pm
Title: The covering method: an intuitive approach to the computation of p-divisibility of exponential sums
Abstract: Exponential sums over finite fields are an important tool for solving mathematical problems and have applications to many other areas. However, some of the methods and proofs of the results are non-elementary. The main purpose of this talk is to present the covering method, an elementary and intuitive way to estimate or compute the p-divisibility of exponential sums, which is particularly convenient in the applications. The covering method allows us to determine solvability of systems of polynomial equations, improve the search for balanced Boolean functions, give better estimates for covering radius of codes, and has many other applications.