My research interests
include topological data
analysis with applications
to dynamical systems and biological
phenomena. I am also interested
in the intersection of
topological statistics and
machine learning. In particular, I am interested
in answering questions related
to the robustness of topological
summaries in noisy systems, the
predictive power of topological
statistics in modeling, and the
effectiveness of topological
quantities as input for machine
learning tasks. At present, I work in a range of
applications including zebrafish
stripe development and evolutionary
I give a very brief description
of my research projects. Feel
free to contact me for more
My research is currently being funded by the National Science Foundation Graduate Research Fellowship Program. Any opinions, findings, and conclusions or recommendations expressed on this website are my own and do not necessarily reflect the views of the National Science Foundation.
Current Research Projects
A Topological Analysis of Model Sensitivity and Classification for Pattern Formation on ZebrafishMy dissertation research is advised by Björn Sandstede and co-advised by Andrew Blumberg. We are interested in applying topological data analysis to study dynamical systems and biological phenomena. Currently I am working on a problem related to classifying model outputs from zebrafish stripe development models. We use topological summaries of the model outputs as input to a classification algorithm. This gives us a way to automatically classify model outputs under various parameter regimes and noise tests. We hope to use this work to better understand these models and the underlying biological mechanisms.
Topological Estimation of Recombination RatesI collaborate with Devon Humphreys and Michael Miyagi under the supervision of Andrew Blumberg on this project. Briefly, we extract topological summary statistics from genomic data and then use techniques from regression analysis to infer hotspots of recombination.
Research with UndergraduatesIn the Summer@ICERM 2017 program I began working with Dr. Katherine Kinnaird and undergraduates Erin Bugbee, Claire Savard, and Jonathan Weisskoff on the cover song task. The goal for this project is to develop a flexible and computationally efficient method for completing the cover song task. We use methods inspired from topological data analysis to correctly match songs which are remakes of the same original piece. This work in ongoing with Katherine Kinnarid, Erin Bugbee, and Claire Savard. Congratulations to Claire and Erin for winning the MAA "Outstanding Poster Award" at the 2018 Joint Mathematics Meeting where they presented our work!
Research GroupProfessor Sandstede's research group participates in weekly meetings each semester where we discuss topics in dynamical systems and related fields. Below is an overview of our meetings along with the presentations I have presented.
|Semester||Main Theme||My Subtopic||Presentation|
|Spring 2018||Probability and Statistics||Classification Algorithms||Lecture and Python Demo||Fall 2017||Dynamics and Statistics||Parallel Computing in Matlab||Interactive demos|
|Spring 2017||Data Science||Methods of Machine learning||Here.|
|Fall 2016||Vegetation Patterns||TDA and Diffusion Maps||Here.|