In this talk, we will delve into the fascinating realm of maximal and supersingular curves, two pivotal concepts in algebraic geometry with significant applications in finite fields. Maximal curves, defined over finite fields, reach the Hasse-Weil upper bound for the number of rational points, positioning them as a subject of substantial interest in both theoretical mathematics and practical applications. Supersingular curves, a special category of elliptic curves, exhibit unique properties that are particularly relevant in the fields of cryptography and coding theory.
