## Analyzing U.S. Migration Data by Gluing Triangles Together

## Meet mathematics major Olivia McGough.

**Hometown:** Corvallis, Oregon

**Thesis adviser:** Prof. Angélica Osorno [mathematics]

**Thesis:** “Persistent Homology and Applications to Graph Data”

**What it’s about:** Persistent homology is a recently developed data analysis tool that relies on theory from topology and is used to extract information about the shape or structure of data. My thesis covers the mathematical theory needed to understand persistent homology and reviews published applications of persistent homology to different data sets. I also run my own data analysis on publicly available U.S. migration data.

**What it’s really about: **What happens if I glue some triangles together?

**Influential professor: **Prof. David Perkinson [mathematics] was an incredibly influential figure during my time at ²Ø»¨¸óÖ±²¥. He let me work with him on a research project the summer after my sophomore year that ended up being a formative experience for me. The goal of the project was to construct a proof of a combinatorial result conjectured by Gopal Goel, one of David’s students. Throughout the process, I learned a lot of math, but more importantly I learned how fun research can be and what I am capable of. He also taught me the importance of good chalk.

**Concept that blew my mind:** There are infinities of different sizes?! Between every two rational numbers (fractions) there is an irrational number, and between every two irrationals there is a rational. However, the probability that a randomly selected number is rational is zero. The set of rational numbers is much smaller than the set of irrational numbers, even though they are both infinite sets.

**Cool stuff:** I’ve been a tutor and course assistant in the math department for three years, which has been a fun job and a good opportunity for me to give back to a department that has educated, mentored, and uplifted me during my time at ²Ø»¨¸óÖ±²¥. I want to emphasize that the ²Ø»¨¸óÖ±²¥ math faculty are truly unmatched, and I will never be able to thank them enough.

**Challenges faced:** I was pretty intimidated by how smart some of my peers were when I first came to ²Ø»¨¸óÖ±²¥, especially in my math classes. For a while I felt like no matter how hard I tried I wouldn’t be able to keep up with them. I spent a lot of time freshman year in math drop-in tutoring and in my professors’ office hours, which was a game changer for me. I still receive tutoring and go to office hours regularly.

**How ²Ø»¨¸óÖ±²¥ changed me: **I’ve definitely gotten gayer. And I have more tattoos. Not sure if I’m smarter but I know a lot more math.

**Awards, fellowships, grants:** I received the Rosenbaum Fellowship to work with Prof. David Perkinson for a summer, and I received the Opportunity Grant to present my research at a conference. For the summer postgraduation, I worked with Profs. Angélica Osorno and Kyle Ormsby in their Collaborative Mathematics Research Group, which is funded by an NSF grant.

**What’s next:** This fall I begin a statistics PhD program at the University of Washington.