Friday January 8, 2016, 1:00 p.m.-5:50 p.m. AMS Special Session on Number Theory and Cryptography, II Room 606, Washington State Convention Center - See more at: http://jointmathematicsmeetings.org/meetings/national/jmm2016/2181_program_ss72.html#sthash.0qhNOcdn.dpuf

I will talk about how the SageMath (http://sagemath.org) software is incredibly useful for number theory and cryptography research.

15 minutes to talk about what SMC provides for writing a paper in practice.

8 min. A research project

• background: mazur-stein-watkins-bektemerov bulletins 2006: give a freshman a student project and see what happens

• crazy plots: the rank just keeps getting bigger in the data

• random matrix heuristics and other conjecture: rank is 1/2 in the limit

• manjul bharghava: the rank definitely doesn't just keep getting bigger!

• challenge: systematically compute the ranks of all elliptic curves BLAH of height BLAH far enough that we can finally see the rank going down!

• here's when it happens

• bonus: some other statistics

4 min. Features of SMC for writing this paper

• collaborative editing of latex documents

• collaborative persistent terminals (e.g., ssh to cluster somewhere)

• edit Python code; run from sage worksheets

• use sqlite easily

• run project on a 32-core big-memory VM at Google

• chat: post little comments on the side of any file being edited

4 min. Features of Sage for writing this paper

1. • mwrank

• Simon Spicer's Elliptic curve enumeration

• Simon Spicer's L-function bounding code

• Magma interface