What a nice thread idea. I'm a first year grad student in "engineering physics". My research focus is plasma physics and magnetic confinement fusion, but right now I'm still mainly trudging through classes. My main expertise is in classical physics, mainly fluid mechanics, electrodynamics, and applied math.

What issues in your domain call most critically for sharp thinking?

In problem solving in our domain there is a need for sharp thinking, but I tend to think that this is actually just an illusion, and the really hard part comes outside of the actual calculations. In doing a calculation you have to kind of figure out what's going on, but usually if you know all the assumptions and the correct methods, this is just a matter of working out the details. The hard part is understanding what assumptions are valid, and knowing what to do when you get stuck.

What do you know that could be of interest to the LessWrong community?

General meta-level thoughts on math and science, mainly. These are philosophical and practical, in the sense of "Why are math and physics so connected?", or "Why is someone good at math?" or "What is the essential difficulty in doing this physics?" These are all questions I've thought about quite a bit in the course of my education.

What might you learn from experts in other domains that could be useful in yours?

I think there is stuff to learn in the basic meta-level philosophical and logical techniques that come into play in the forum, for example, when people break down other arguments or address flaws in reasoning. I wish I had more practice in things like basic logic and argumentation (e.g., the different types of argument.) It's very useful for physics and especially math, which relies on the fidelity of your reasoning process.