University of Michigan Student Arithmetic Seminar

Date:	Speaker:	Title:	WebVideo:
9/8/2010	Alex Mueller	Organizational Meeting	None
9/15/10	Zachary Scherr	Continued Fractions in Function Fields	None
9/22/10	Hunter Brooks	Introduction to the Arithmetic of Elliptic Curves	None
9/29/10	Ari Shnidman	Intro to Modular Forms	None
10/6/10	Alex Mueller	Hypergeometric Functions Over Finite Fields	None
10/13/10	Tom Ngo	The Mordell-Weil Theorem	None
10/20/10	Julian Rosen	Transcendental Numbers	None
10/27/10	Suchandan Pal	The Cohen-Lenstra Heuristics	None
11/3/10	TBA	TBA	None
11/10/10	Err'body	Conference Practice Party	None
11/17/10	Zachary Scherr	Lehmer's Conjecture	None
11/24/10	Turkey Man	The Turkey Function	None
12/1/10	Ari Shnidman	Galois Representations	None
12/8/10	Jeremy West	Surprising Open Problems	None
12/15/10	TBA	TBA	None

9/8/10

Planning Meeting

Come prepared with ideas for talks you would like to give or talks you would like to hear.

9/8/10

Introduction to the Arithmetic of Elliptic Curves

Among the most important objects of study in algebraic number theory are the elliptic curves. These very classical geometric objects have, on the one hand, a simple enough explicit description that they are amenable to concrete calculation, and on the other, enough internal structure that they provide deep insight into otherwise hopeless monstrosities like the absolute Galois group of Q. We will give somewhat of a crash course in the arithmetic of elliptic curves. The only prerequisites are Galois theory and a passing acquaintance with projective space over a field.

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