• chatted with Lei about log stuff
• Some feedback on research statement

https://math.berkeley.edu/~ogus/preprints/logrihfordocumenta.pdf

Ogus is writing in a gentle pleasant way.

• First, smooth proper complex manifold. Local system corresponds to vector bundle with flat connection.

Q: hold on, what is the statement? Suppose $(E_{top}, \mu)$ is a (topological) vector bundle with monodromy, and this goes to $(E_{an}, \nabla)$ a holomorphic vector bundle with integrable connection. Then, if we vary $\mu$, does $E_{an}$ change or just $\nabla$ change?

Got some feedback from a professor about my research statement writing. I am sharing it here so it might benefit others. Indeed, I might focus too much on the concrete details, rather than giving context about why and how.

It is not enough to simply list all the things you did, however great they are. You need to show you have an important research program — to give people a context for your results, and also to convince them you are work will continue to bear fruit. All these things are true for you, but unless you have experts sitting on the hiring committee, and enough of them, people need help parsing the significance of what is being done. The letters can do this for you to some extent — but it does not change the fact you miss an opportunity to make a strong case for yourself. You want to convince people the problems you have worked on are really deep and important, and so is your contribution. Moreover, once you do become faculty, you will need to continue making cases for your research — to granting agencies, and at promotion steps. So, showing you know how to make an effective case, is really important.