How far along are you in graduate school? What exactly is it that you do? These are two questions I'm asked frequently these days and am happy to answer. I created Math3ma precisely for my time in graduate school, so I thought it'd be appropriate to share the answers here, too, as a quick update! First,
I'm graduating this semester!
It's exciting. I've really enjoyed my time as a graduate student and have been looking forward to the future for a while now. (I'll share more on my post-graduate plans in another post.) In the mean time, I'm in the midst of writing up my dissertation. It's in the photograph above. The title is pending. Stay tuned!
Now to the second question: "What's your research about anyways?"
My work doesn't fit into any one mathematical label (geometry, topology, algebra, category theory, etc.), so it's hard to answer this question with just one or two words. I'm using different ideas to make connections across different things! And I love it for that reason. I'll elaborate.
I'm in a pure mathematics program, but some of the most exciting mathematics is, to me personally, that which is inspired by cross-discipline communication. I am most deeply moved by mathematics that is motivated by some phenomena in nature, or in physics, or in an applied setting.
Amazingly, my thesis is in this very space! (Just three years ago, I didn't know I'd be doing what I'm doing now, hence "amazingly." It's a very cool story, but I'll save it for another day.)
My current work is in pure mathematics, motivated by a concrete problem in machine learning. What's more, the mathematical tools are borrowed from physics. A lot of the ideas are already shared here on Math3ma. There's lots of linear algebra, some probability, some category theory, and there's an application to natural language using tools called tensor networks.
More concretely, I've been working on modeling probability distributions with certain linear operators called density operators. The pure mathematics is interesting in its own right—and it stands on its own—but it was originally motivated by a quest connected to natural language along with the realization that ideas in physics can provide the model with lots of theoretical clarity.
See? A mixture of things! It's great.
I'll say more as I get closer to finishing the dissertation. Just wanted to duck in and share a quick update.
Now, back to writing!