I am a Teacher-Scholar Postdoctoral Fellow at Wake Forest University in North Carolina and work with Kenneth Berenhaut. I enjoy thinking about questions such as:
- How can we understand the community structure of data? What is the meaning of local? What do we mean by clusters?
- Can simple (socially-inspired) local rules for a random walk on a network lead to interesting global properties?
- Where do (finite) random walks on a network take us? In what ways are those reached central?
- Suppose that, rather than numeric distances, we only have distance comparisons (among triples of points). How can we effectively leverage that limited information? What kind of structure is required for interpretability?
- Can we articulate measures of the degree of unpredicability of a process given that we can only witness a single (relatively short) sequence of outcomes?
Broadly speaking, the questions I’m interested in these days are in discrete applied probability and are motivated by a social perspective. My thesis work at Dartmouth (advised by Sergi Elizalde) was focused on combinatorial problems arising from permutation-based approaches to time series analysis and its connections to classical discrete dynamics.
The picture below helps us visualize the strong and weak relationships among rather high-dimensional points, revealing distinct clusters in this setting. The perspective we take is socially-based – and is also entirely free of parameters, iterative procedures and distributional assumptions. If you’d like to hear more, send me an email and we can chat (and perhaps apply it to any data you have, lots more coming soon).