Resources

Here I’ll post a repository of some things that I’ve written and some other links. This list will be continually updated.

Papers/Preprints

1.On the stability and algebraicity of algebraic K-theory. arXiv version. Note that the arXiv version is usually not up-to-date. This paper provides a new definition of the K-theory of stable ∞-categories as a functor that takes values in stable ∞-categories. The K-theory of an ∞-category of modules is also computed. I submitted this to Intel ISEF 2015. (Note: the actual paper that I submitted is here. The above paper is the shortened version containing only the research aspects of my paper, while the last link is the full 116 page paper in its full glory, i.e., including all the preliminaries, index, etc.) Here’s a super brief summary of the paper which I prepared for a science fair.

2. Mathematics of the Theory of Black Holes. This expository paper reviews the notion of a “singularity” through mathematical methods (differential geometry). It’s meant for someone who’s had a graduate level course in general relativity. (I guess it could be thought of as an “end-of-term” paper.) At the time of writing this paper, I hadn’t studied differential geometry in over a year, so any mistakes (and there will be quite a few) are mine.

3. Here are my notes on the theory of ∞-operads – I don’t think these contain any mistakes. To complement this, here are my notes on the theory of (∞,n)-operads, with only n=2 actually discussed.

Awesomeness

Marcy Robertson, my mentor at UCLA.

Noam Elkies, a professor at Harvard who’s helping me learn algebraic number theory.

Not-so-much-awesome-awesomeness

Me. That’s a link to my homepage.