January 16, 2024

**Title:** *Three proofs of quadratic reciprocity and their influence on twentieth century mathematics*

**Speaker:** Clemens Berger (UniversitĂ© CĂ´te d'Azur)

This expository talk is an invitation to revisit the quadratic reciprocity law as formulated by Euler and Legendre in the 18th century and proved by Gauss in the first half of the 19th century. We discuss three different proofs: a combinatorial, a Galois-theoretical and an analytical. All three can be traced back to one (or several) of the eight proofs of Gauss but have since then been simplified considerably thanks to the joint efforts of many well-known mathematicians. The employed methods had a profound influence on twentieth century mathematics and many of them are nowadays a vital part of the undergraduate program in mathematics.