I worked a bit today on building new capabilities for Kepler and TESS and everything to follow: In one project, we are imagining getting parallax information about stars in Kepler. This has been tried before, and there are many who have foundered on the rocks. We (meaning Foreman-Mackey and I) have a new approach: Let's, on top of a very flexible light-curve model, permit a term proportional to the sine and the cosine of the parallactic angle. Then let's consider the amplitude-squared of those coefficients as something that indicates the parallax. The idea is similar to that of the "reduced proper motion" method for getting distances: No proper motion is a parallax, but closer stars tend to have higher proper motions, so there is work that can be done with them. There the stochastic component is the velocity distribution in the disk. Here the stochastic component is the unmodeled flat-field variations.
In the other project I worked on today, I figured out how we might switch asteroseismology from it's current mode (take data to periodogram, take periodogram to measurements of mode frequencies and amplitudes; take mode frequencies to big and small differences; do science on the frequency differences) to one in which the most important quantity—the big frequency difference—is observed more-or-less directly in the data. I have a method, based on Gaussian Processes and Fourier transforms that I think might possibly work. One cool thing is that it might just might enable asteroseismology measurements on dwarf stars even in Kepler long-cadence data. That would be insane. Both of these projects are also great projects for TESS of course.