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.
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
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
Simon Spicer's Elliptic curve enumeration
Simon Spicer's L-function bounding code