Friday, October 31, 2008

Annals, Crypto, and Modular Forms

This morning I read Iwasawa's original paper where he introduces p-adic L-series of Dirichlet characters. I basically read this on a whim, since I saw it in a friend's collection of scans.

I also skimmed through all the number theory related papers published by Annals of Math during the last few years. Probably the most interesting were Kartik Prasanna's paper on integrality of Petersson norms (vol. 163, 2006, 901-967), in which he remarks "I am grateful to my advisor Andrew Wiles for suggesting the problem mentioned above and for his guidance and encouragement. The idea that one could use Iwasawa theory to prove the integrality of the Rankin-Selberg L-value is due to him and after his oral explanation I merely had to work out the details." Very humble. Another very nice paper is the fourth in Manjul Bhargava's sequence of papers about parametrizing quintic rings. There's also a nice paper by H. Darmon about his p-adic version of Heegner points.

After that I read through half my paper on generalizing the Gross-Zagier formula, and marked it up with comments.

Then I met with some "Dutch crypto guys" from Microsoft Research and had lunch. After that I went to Clement Pernet's class, where he explained Weiedemann's algorithm for computing minimal polynomials of pairs (A,v) where A is a sparse matrix and v is a vector.

Next I went to the new Number Theory and Computation seminar that Dan Shumow and I started, and saw a nice talk by Dustin Moody on how pairings provide new techniques for algebraic crypto. Next Craig Citro gave an exciting and erudite talk on enumeration of mod p modular forms, which develops in great details some ideas I discussed with him at Sage Day 7 at IPAM. I gave Craig a hard time during his talk though :-).

Now I'm dressed up as a skateboarder for Halloween.

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