Fun with Quadratic and Cubic Reciprocity

Time for another math club meeting! Rhombus!

This time we have Paul Pedersen, who you may know from the Silicon Valley Math Meetup (https://www.meetup.com/Silicon-Valley-Math-Meetup/). (https://www.meetup.com/Silicon-Valley-Math-Meetup/).) I was fortunate enough to have made his talk on Galois Theory in the Fall of last year, and was inspired to get him to come give a talk here in SF. Paul managed to exhibit the beauty and essence of Galois Theory very accessibly in the course of about an hour and a half.

Blurb:

"Quadratic Reciprocity was Gauss's favorite theorem. According to MathWorld (http://mathworld.wolfram.com/QuadraticReciprocityTheorem.html) he devised no less than 8 different proofs of this theorem. Let's find out what makes reciprocity laws so fascinating. By now there are hundreds of independent proofs of quadratic reciprocity, and not a single one of them is 'obvious'. The two most interesting approaches use (1) Gauss sums, and (2) algebraic field extension. Case (2) is the one that generalizes to cubic and quartic reciprocity. I'd like to walk through the proof of cubic reciprocity in detail. A good reference is Ireland and Rosen: "A Classical Introduction to Modern Number Theory". With some luck, we can get to the point where the statement of Eisenstein Reciprocity at least makes sense."

NB: With construction in the Noisebridge building now finished and with the event taking place in Turing Room (which has four complete walls), we should be spared the ambient noise problems from last time.