Everything is almost lined up. The statements are written, minus some editing of the research statement. My letter writers are lined up. The first draft of the paper Steve and I are working is done. The next phase is to do more research on the universities I am going to apply to and work up cover letters. There are so many things to do right now, but they are all full of strange small tasks. Oh yeah, I am giving three talks at UNT this semester, attending a set theory workshop at UIC in a a few week, and speaking at Ohio University in November.
Research wise, Steve and I finally cracked the code between infinitary logic and infinity Borel codes. That completed the last gaps on our purely descriptive set theoretic proof of the Harrington-Shelah theorem. Moving forward, we will be applying these tools to try and generalize the Harrington Kechris Louveau theorem.
I'm going to work up a series of posts about Silver's theorem and how it generalizes. The first one should be up tonight.
Ugh I let writing cover letters take SO much time. It was hard to find good information on so many university websites. So unless you know someone there, it's hard to have something specific to say about why you're a good fit. But having been on the other side now, I can say - at least at smaller schools/departments - they will expect your cover letter to include something specifically relevant. Sometimes there are hints in the job description about what they're looking for, so try to read between the lines on the job ad if you don't have much else to go on. Good luck!
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