Abstract: The now proven Weil conjectures had a profound influence on number theory and algebraic geometry in the last century. The first of the conjectures was proven by Dwork in 1960 using an ingenious application of exponential sums and p-adic analysis. Exponential sums lie at the heart of many proofs in number theory, such as one of Gauss' proofs of quadratic reciprocity. In the years following Dwork's proof, it became apparent that studying families of exponential sums yielded further insights. In this talk, we will discuss a few of these insights.
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