Comments on: Mock-up research thread http://polymathprojects.org/2009/07/26/hello-world/ Massively collaborative mathematical projects Sun, 19 May 2013 02:40:38 +0000 hourly 1 http://wordpress.com/ By: New polymath blog, and comment ratings « What’s new http://polymathprojects.org/2009/07/26/hello-world/#comment-86 Tue, 28 Jul 2009 19:20:16 +0000 #comment-86 [...] the ball rolling on this blog with some proposed rules for running a polymath, a mock-up of what a research thread and a discussion thread for a project would look like, two new proposals for the next polymath [...]

]]> By: Terence Tao http://polymathprojects.org/2009/07/26/hello-world/#comment-4 Sun, 26 Jul 2009 20:19:14 +0000 #comment-4 Here is a second comment, not directly related to comment #1. “What if we try a dyadic model first, for instance replacing the real line by the p-adics for some small p, e.g. p=5? One could hope to then do some sort of induction on scales argument, perhaps using Bellman functions.”

]]> By: Terence Tao http://polymathprojects.org/2009/07/26/hello-world/#comment-3 Sun, 26 Jul 2009 20:18:17 +0000 #comment-3 This is a test of comment nesting: a response to Comment #1. “It looks like the Fourier representation of T is of the form

\widehat{T(f,g,h)}(\xi) = C \int_{\xi_1+\xi_2+\xi_3=\xi} \hat f(\xi_1) \hat g(\xi_2) \hat h(\xi_3) \hbox{sgn}(\xi_1+2\xi_2+3\xi_3)

for some absolute constant C, where the integral is over the plane \{(\xi_1,\xi_2,\xi_3): \xi_1+\xi_2+\xi_3=\xi\}. Note that if one dropped the signum factor (and the constant C), this would be the formula for the Fourier transform for the pointwise product fgh, so perhaps it is good to think of T(f,g,h) as a variant of the product fgh.”

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]]> By: Terence Tao http://polymathprojects.org/2009/07/26/hello-world/#comment-2 Sun, 26 Jul 2009 20:10:36 +0000 #comment-2 This is a test comment: “What would the trilinear Hilbert transform look like in terms of the Fourier transform \hat f(\xi) := \int_{\Bbb R} f(x) e^{-2\pi i x \xi}\ dx?”

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