WHAT IS AN ELLIPTIC CURVE? presented by Fabian Ramirez, UC Irvine

Assuming you are working over a field, F, of characteristic >3, an elliptic curve is the solution of an equation of the form y^2 = x^3 + ax + b where a,b are in F with 4a^3 + 27b^2 being nonzero and a specialized point at “infinity.” In modern mathematics, elliptic curves are everywhere. “Semistable” elliptic curves played a fundamental role in Wile’s proof of Fermat’s Last Theorem. Similarly, Elliptic Curve Cryptography underlies the security of popular apps such as WhatsApp and Apple’s iMessage. However, at first glance, it is not clear why a humble-looking cubic of the above form is so important, and a quick Google search is no help with elliptic curves often described as “projective nonsingular algebraic curves of genus one.” Many of these words are meaningless without an entire graduate course in algebraic geometry. The goal of this talk is to create a bridge between the math often taught in a standard undergraduate program and the fascinating world of elliptic curves.

In Person: Darwin 103, Virtual: bit.ly/SP24_math_talks

For more information, including the complete list of this semester's speakers, visit our website: https://math.sonoma.edu/math-colloquium.