Cam's Blog

December 16, 2010

Back from New York

Filed under: Math, Travel — cfranc @ 9:47 am

I’m back in Montreal after spending two days in New York working with Marc. We fixed up our p-adic integration work in Sage. It needs a lot of work still: we’d like to implement Coleman integrals, the ability to compute values of anticyclotomic p-adic L-functions and a few other odds and ends. It also needs to be optimized and (gasp!) documented… but it’s getting to a very usable state.

Just before I left we tried to use our routines with rigid analytic modular forms to compute equations of Shimura curves, following a suggestion of Darmon. Our code is too slow at the moment to recognize the equations we find as rational, and not just p-adic, but we’re hopeful that with some tweaking it should give a reasonable algorithm, at least for low genus curves. I may say more about this after we’ve had some time to work this stuff out and write it up!

New York was fun but I didn’t get to see much of it. We spent nearly 30 out of 48 hours working straight, breaking only for food and sleep. As Marc pointed out to me, though, I can still say I did some sight-seeing, as “Visit Columbia University” is a suggestion in all of the New York guide books…

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