Grants

My research is currently being funded by the National Science Foundation Graduate Research Fellowship Program.

Current Research Projects

Research with Undergraduates

Comparing Songs without Listening

In the Summer@ICERM 2017 program I worked with Dr. Katherine Kinnaird, Erin Bugbee, and Claire Savard on the cover song task. The goal for this project was to develope a flexible and computationally efficient method for completing the cover song task. We used methods inspired from topological data analysis to correctly match songs which are remakes of the same original piece.

Reading Group

Professor 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
Fall 2016 Vegetation Patterns TDA and Diffusion Maps Here.
Spring 2017 Data Science Methods of Machine learning Here.

Past Research Projects

A Topological Analysis of Targeted In-111 Uptake in SPECT Images of Murine Tumors

I worked under the supervision of David Damiano for my undergraduate thesis at The College of the Holy Cross. We developed a novel topological method of analyzing Targeted In-111 Uptake in SPECT Images of Mouse Tumors. The motivation for this method is illustrated in the videos below. These videos show the super levelsets of images of murine tumors as we descend through a filtration of tumor uptake values. The video on the left corresponds to the mouse tumor at hour 24 in the study, and the video on the right is the same tumor at hour 72. Our method captures the topological information of these filtrations of the tumors across a time series of images and surpasses standard techniques in their ability to capture tumoar heterogenity. You can find our paper here.



Assimilating Eulerian and Lagrangian data in traffic-flow models

During the summer of 2014 I participated in a research project on data assimilation for traffic flow through a Research Training Grant on “Integrating Dynamics and Stochastics.” I worked under the supervision of Björn Sandstede and collaborated with Courtney Cochrane, Joey DeGuire, Bridget Fan, Emma Holmes, Patrick Murphy, and Jenna Palmer. Our graduate mentors were Paul Carter, Laura Slivinsky, and Chao Xia. You can find our paper here.