Projects
•
Exposition: Why the world will not end if Cubs win the 2015 World Series
( code)
•
Who's On First: Predicting baseball batterpitcher matchups
( code)
• More projects coming soon!
Math
Overview
My research is (or was) focused on probability and combinatorics,
specifically representation theory methods in the study of Markov chains.
Highlevel summary: Fourier transforms convert convolutions of probability distributions
in the time domain to pointwise products in the frequency domain, and the frequency domain for a nonabelian group
is given by its group representations, so we can track the mixing of a Markov chain by observing the Fourier transform
of the transition probabilities on the representations of the underlying group, which in turn can be quantified
by computing and summing the characters of the representations.
Higherlevel summary: I study card shuffling.
Additionally, I am deeply and eternally interested in number theory, though preferably without algebraic geometry.
Papers
Tensor powers of the defining representation of $S_n$,
J. Theoretical Probability, 30:3 (2017).
A Random Walk in Representations, PhD thesis (2014).
Smallest irreducible of the form $x^2dy^2$,
Int. J. Number Theory, 5 (2009).
Fourier Analysis in Number Theory, Senior thesis (2008).
Notes
ProbabilityStochastic processes
Representation theory and Markov chains
Miscellaneous
• For the section of Penn Math 240 that I taught in Summer 2011:
syllabus

notes

tests

quotes.
• For my PhD qualifying exam in April 2010:
syllabus

transcript.