“Summer research was incredibly fun and has strengthened my interest in mathematics.” — Esha Datta

Esha Datta ’17
Palo Alto, California
Economics, Mathematics

I worked in a team of Macalester and Harvey Mudd undergraduates to evaluate systems of oscillators using topological data analysis. An oscillator is anything that exhibits periodic behavior. Examples include neurons firing or metronomes ticking. We were advised by math professors Chad Topaz and Lori Ziegelmeier from Macalester and Andrew Bernoff from Harvey Mudd.

My research focused on coupled oscillators, which are oscillators that are influenced by the behavior of other oscillators around them. Coupling can cause groups, or systems, of oscillators to synchronize over time. This is seen in nature with fireflies; fireflies will initially flash at their own frequencies but can eventually begin to flash in unison.

We studied a famous model that describes such behavior, the Kuramoto model, through the lens of topological data analysis (TDA). TDA is a new field in applied mathematics that studies the shape or structure of a dataset. This allowed us to evaluate how systems of coupled oscillators in the Kuramoto model move and change over time. Using TDA, we gained a better understanding of the synchronization behavior of oscillators in this model.

Research was extremely challenging, but gave me a chance to apply what I’ve learned in my time at Macalester. I used MATLAB software to simulate the systems of oscillators and measure their synchronization. My team and I presented to the rest of the math researchers throughout the summer, which allowed us to share our progress and develop the skills necessary for a career as a mathematician. Our research culminated in a paper that outlined our findings and a large amount of code that future researchers can use to further pursue this topic.

The most rewarding aspect of my summer research was the opportunity to work alongside my professors. They were happy to advise us when we were confused, and also to answer questions we had about pursuing mathematics after Mac.

September 28 2015

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