The new year is upon us, and though I am not a fan of traditional resolutions, I do believe there is utility in writing down one's goals in an accessible place and returning frequently to analyze progress.
If I don't finish these things, I'll be quite sad by the time arrives. Here's the list:
Complete at least 1/3 of the exercises in Chapters II and III of Hartshorne.
Complete the preliminary exam and course requirements for the Ph.D.
Work through most of Fulton's Introduction to Toric Varieties
Understand the log geometry portion of "Decomposition of degenerate Gromov-Witten invariants"
Choose an advisor
I've been working through Hartshorne sporadically over the past two years. It's time to wade through it earnestly. There are a total of 222 exercises between chapters II and III of Hartshorne, so I'll need to complete 74 exercises by May. That's about 2 exercises every 3 days.
UT Austin's math Ph.D. program requires students to complete 7 preliminary courses in order to advance to the second stage of the Ph.D., and at least 3 of those courses by exam. I've finished one exam and two courses at the time of this writing. I think I'll receive credit for 3 courses I completed at Utah and will take two more exams in January. If everything goes perfectly then I will be done quite soon, but in the likely scenario in which I fail at least one of the exams, I will need to study and retake it in either June or August. If I am done with this stage of the Ph.D. by Fall 2023, I'll consider that a success.
I'm going to help run the Beginner Algebraic Geometry Seminar (BAGS) during the Spring of 2023 (see the seminar webpage). Our primary goal is to work through the majority of Fulton's toric varieties textbook.
I suspect log geometry will be the topic of my eventual thesis and would like to understand more about it by the end of 2023. The above paper is a bit of a beast, but understanding a piece of it seems reasonable and is a more actionable goal than "understand more log geometry".
This one is self explanatory.
These would be nice things to do, but are either not vital for my advancement towards a Ph.D. or can be completed in the future.
Complete publishable work on Ising computation
Become more familiar with two of the following programming languages: Julia, Rust, Haskell, Go Lang.
Find a preliminary research topic
Complete a machine learning project