What is your research?
I study heat flow and problems in math and physics using techniques of pure math. Most of the time I work on a problems that have physical motivation. My main interest is in the mathematical techniques that are used to tackle these problems.
Here is one example of a problem. Imagine a perfectly square room with perfectly insulated walls, so no heat can enter or leave the room. Now draw 16 floor tiles: half generate heat, and the other half absorb heat.Then create a second room, with the same size and insulation as the first. Move all of the hot tiles together in each column. The conjecture is that the second room will have a larger gap between the maximum and minimum temperature than the first. I proved this correct a few years ago, and I’m currently working on writing up my solution for the same problem in higher dimensions.
The most interesting part of my research to me are the techniques I use to solve these problems. I’m not a physicist, but I like to think I have good intuition for solving the problems.
What do you do when you get stuck?
If I get stuck with this research I try one of two things. First, I can try to solve an easier problem. Sometimes, solving that problem will give me insight or techniques that can carry over to the harder problem. Another option is to search the literature for similar problems. I focus my attention on the techniques that other researches use and try to adjust them to fit in my situation. Sometimes, I get lucky, and find something useful.
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