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Wednesday, November 20, 2019

**Abstract:** The theory of algebraic curves over a finite field runs entirely parallel to the classical theory of number fields (finite extensions of the rational numbers). Analogues of many results that are long standing open conjectures in the number field case are theorems in the case of curves over finite fields. We will introduce the key concepts in this area, survey important results and (time permitting) state some original results. This talk assumes only a passing familiarity with finite fields.