I always keep an eye on the Polymath Projects, ever since I became interested in Polymath 4 (link to Polymath4 wiki). While I worked on Polymath4 as an REU student under Dr. Croot, I fell upon a method to ‘quickly’ count the number of lattice points under a quadratic (with no linear term and rational coefficient). Unfortunately, it didn’t lead to direct improvement, so I didn’t post it on the wiki.
But I did a short write-up of the method, and it’s here: Points under Parabola.
At some point, I’ll try to write it up on this blog proper.