ESP Biography


Major: Math and Physics

College/Employer: Columbia University

Year of Graduation: 2021

Picture of Eli Fonseca

Brief Biographical Sketch:

Not Available.

Past Classes

  (Clicking a class title will bring you to the course's section of the corresponding course catalog)

M770: Primes of the form x^2+ny^2 in Splash Fall 2018 (Oct. 28, 2018)
This course will explore which primes can be represented as $$x^2+ny^2$$ with $$x,y$$ integers and $$n$$ a natural number. Despite the questions simple appearance finding a complete answer is anything but simple as it requires a deep understanding of field class theory, modular functions, and complex multiplication. After introducing some basic preliminaries we will focus on the simpler case of $$n=1$$. I will present a constructive proof, due to Euler, which fully answers the question in this simpler case. Then we will turn our attention to the more general question by looking at a few more special cases and then present a theorem, due to Weber, that answers the general question without proof.