Here are slides for the talk.

# Applied Math Seminar at Dartmouth

Here are slides for the talk.

A pre-print for the last third of the talk will appear shortly.

# Brandeis Combinatorics Seminar

Here are the slides for the talk, given with a focus on applications of these results to time series analysis.

# New York Combinatorics Seminar

Given a time series, we can extract a collection of permutations of a fixed length by sliding a window across our data and recording the relative order of the values in the window. It is known that the distribution of permutations that appear conveys information about the complexity of the time series; one commonly studied measure is permutation entropy. Interestingly, in the specific case that the time series is defined by iterating a piecewise monotone map of the interval, there are forbidden permutations. Moreover, the number of allowed permutations encodes the system’s topological entropy, a measure of complexity that is itself closely related to the permutation structure of periodic points.

Using permutation-based measures of entropy in time series analysis as motivation, I will talk about some interesting problems that arise at this intersection of combinatorics, dynamics and time series analysis.

# Summer Combo in Vermont

# FPSAC 2017

Here is a link to the extended abstract “Patterns of Negative Shifts and Signed Shifts” and a PDF of the poster.

# Permutation Patterns

Here are the slides for the talk I gave during Permutation Patterns 2017.

Here is an extended abstract about Patterns and Cycles in Dynamical Systems.

# Brandeis Combinatorics Seminar Talk

Here are the slides from this seminar talk.