To Do List

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Current Projects / To do list

We need to come up with some organization for the articles.

The list below can be a starting point to click on links and edit each page. The following are some of the topics that should appear in this wiki.

  • A sort of Starting page that serves as a "root" for all pages we add (ideally, any page we create should be reachable from here). (UPDATE: See discussion.)
  • Fractional curvatures in conformal geometry.
  • It would be wise (once the wiki is more mature) to add pages about the Boltzmann equation, since it is one of the more "classical" and better known integro-differential equations.
  • Pages about Homogenization (local and nonlocal) should appear here too.
  • Given the recent works of Osher/Gilboa and Bertozzi/Flenner on Ginzburg-Landau on graphs we should have an article on the natural similarities between non-local operators and elliptic operators on graphs.

We may want to include a mini second order elliptic wiki inside this wiki.

We may want to have a section on open problems, for example integral ABP for general kernels, harnack for kernels with a less restrictive bound below, $C^{1,\alpha}$ estimate in bounded domains with a nonsmooth kernel, supercritical quasi-geostrophic, classification of nonlocal minimal cones, etc...

  • Fill up the list of upcoming events such as conferences, workshops, summer schools.

  • A reminder for later (to make a full article out of this): it has become clear (only now, although in hindsight its trivial) that what physicists call "strong interactions" is the same as "very non-local". Namely, strong interactions correspond to forces that approach infinity much, much faster than say Coulomb's force as the distance between two particles goes to zero, mathematically, this means the interaction kernel $k(x,y)$ goes like $|x-y|^{-\gamma}$ for a very big positive number $\gamma$.
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