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.
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# 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