This course is a semester long graduate level reading course on elliptic curves, with emphasis on arithmetic and number theory. The textbook for the course is Joseph Silverman's "Arithmetic of Elliptic Curves." Topics include the Riemann-Roch theorem, elliptic curve point addition, isogenies, endomorphisms, Weil pairing, curves over local and finite fields, and (time permitting) modular curves.
Participants will be expected to give lectures on in-depth topics that complement and reinforce the weekly readings.