# Shanshan Ding

## Math

### Overview

My research is (or was) focused on probability and combinatorics, specifically representation theory methods in the study of Markov chains.
High-level 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 non-abelian 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.
Higher-level 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 $x^2-dy^2$, Int. J. Number Theory, 5 (2009).
Fourier Analysis in Number Theory, Senior thesis (2008).

### Notes

Probability
Stochastic 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.