Wednesdays, 7:30pm; Room TBD, Mathematics
Topic: Elliptic Curves
Texts: J.S. Milne, Elliptic Curves, http://www.jmilne.org/math/Books/ectext5.pdf
Joseph H. Silverman, The Arithmetic of Elliptic Curves
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Date  Speaker  Title  Abstract  Notes 
June 7 
Adam Block

Introduction to
Elliptic Curves

I will lay much of the mathematical groundwork we will need moving forward in the summer. I will discuss intersection numbers, Bezout’s Theorem, projective geometry, and such. I will also introduce the group law on an elliptic curve and, if I have time, prove that we do, indeed, get a group.

Talk Notes 
June 14 
Theo Coyne

Elliptic Curves and Complex Tori

We will introduce lattices in the complex plane and realize complex tori as quotients of the complex plane by lattices. Using the Weierstrass $\wp$function, we will see that elliptic curves over $\mathbb{C}$ are algebraically and analytically the same as complex tori. We may also study the endomorphism group of complex elliptic curves, time permitting.

Talk Notes 
June 21 
Willie Dong

Reduction of an Elliptic Curve Mod p 
In this talk, I will discuss the reduction of an elliptic curve mod p, and, time permitting, go back to the contents of Theo’s talk and draw a relation between elliptic curves over $\mathbb{C}$ and the KdV equation.

Talk Notes 
June 28  Matthew LernerBrecher  Elliptic Curves and their Formal Groups 
In this talk, I will introduce formal groups and some of their basic properties. Using the Weierstrass equation, I will then show how we can construct the formal group associated with an elliptic curve E. Time permitting, I will also discuss the height of elliptic curves.


July 5 

No meeting 


July 12  George Drimba  Heegner Numbers and Almost Integers  We will survey the theory of elliptic curves with complex multiplication and explore the jfunction in order to find answers to arithmetic questions.  
July 19 



July 26 


August 2  
