This page collects expository notes, presentations, and derivations that I've written on various topics in mathematics and physics. Use the subject filters below to narrow the collection.
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I wrote a brief two slide outline of regularization, where the asymptotic expansion of a divergent series can be smoothed out and an unambiguous finite value can be assigned to the series. I also made a series of pedagogical exercises that walk you carefully through explicit examples and teach you how to actually perform regularization. The exercises are a lot of fun, I promise.
TO COME SOON: more detailed notes in standard format.
A self-contained proof of the law of the unconscious statistician , an often-overlooked (but incredibly fundamental) result in probability theory that allows one to easily calculate expectation values of functions of random variables.
A brief note on how to "stack" different exponential distributions together and represent them collectively as a single exponential distribution plus a branching probability. This allows for more efficient simulation of multi-exponential processes in Markov chain applications.
A presentation introducing the basics of sampling from arbitrary probability distributions. Topics include the usual rejection sampling, MCMC sampling, and inverse transform sampling, as well as introducing some ideas I have about using area-preserving maps to sample from arbitrary polygons.
A self-contained note that cleanly presents out the Euclideanized version of $\mathcal{N}=2$ gauged supergravity with an arbitrary number of vector multiplets, and in particular clearly spells out all supersymmetry variations. Then, specializing to the STU model, the notes calculate the on-shell action of various asymptotically-locally AdS${}_4$ BPS solutions, with the goal of deriving new solutions and finding a general formula.
A presentation I gave in March 2019 for a weekly string theory lecture series hosted between a consortium of Belgian universities. The slides are a pedagogical overview and explanation of the results of a fun paper I co-authored on a network-theoretic approach to understanding black hole microstate tunneling in string theory.
A self-contained overview on how the weak gravity conjecture can rule out large-field axion models of inflation.
Lecture notes, discussion questions, and exercises aimed at teaching general relativity to high-school students. I co-authored these as part of a course I co-taught through the Michigan Math and Scholars program at the University of Michigan. These notes are the initial draft version before getting published as a full textbook by Springer, as part of their SpringerBriefs in Physics series.
A brief overview I made of the $g-2$ experiment at Fermilab for measuring the anomalous magnetic moment of the muon. At the time, it was an exciting possibility for a window into new physics, and I discuss the implications of some stringy scenarios. Since this presentation, though, the $g-2$ experiment has wrapped up, ultimately finding finding no tension with the Standard Model, making these slides somewhat useless. It was a fun talk to give, though.
A series of problems sets, solutions, and notes I made while teaching the discussion section of a master's level course on general relativity while at KU Leuven. It includes:
A quick review on the difference between classical and quantum systems, aimed at delineating the criteria for when you can treat a system classically and when you must treat it quantum mechanically.
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