The polymath blog

July 26, 2009

Filed under: discussion,mock-up — Terence Tao @ 8:06 pm

This is a mockup of what a discussion thread for a polymath project would look like; it would run alongside the research thread, but is focused on strategy, exposition, and discussion by casual participants, as opposed to the more cutting edge research conducted by more active participants in the research thread.

Please feel free to make suggestions in this thread as to how the format and organisation of these projects (or this blog) could be improved.

Filed under: mock-up,research — Terence Tao @ 7:27 pm

This is a mock-up of what a research thread for a polymath project would look like.  The thread would begin with a statement of the research problem, e.g.

Problem (Boundedness of the trilinear Hilbert transform). Show that the trilinear Hilbert transform $T(f,g,h) := p.v. \int_{-\infty}^\infty f(x+t) g(x+2t) h(x+3t) \frac{dt}{t}$ is bounded from $L^{p_1}({\Bbb R}) \times \ldots \times L^{p_3}({\Bbb R}) \to L^p({\Bbb R)}$ for some $p_1,p_2,p_3,p$ (e.g. $p_1=p_2=p_3=4$ and $p_4 = 4/3$).

Some discussion of the precise objective (are we aiming for an actual proof, or would we be happy with understanding why the problem is difficult?) would go here.  [Note: while the above problem is an important open problem in harmonic analysis, I am not actually proposing to solve it by polymath here; it is only being used as an example for the purposes of this mock-up.]

A brief discussion of prior results would also be appropriate here, though an extended bibliography might be better placed on the wiki.

A reminder of the polymath rules might also be placed here, together with a link to the discussion thread for issues relating to exposition, strategy, and other meta-comments.  The initiator of the project should also put some effort into laying down preliminary thoughts of the project as clearly as possible.

All threads in a polymath project would have a dedicated category; in this case, the category is mock-up.

Finally, one should put a list of moderators of the project, who would be able to respond to technical issues, such as fixing up a mangled comment.  For this mock-up project, the moderators are:

• Terence Tao (tao@math.ucla.edu)

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