I am Kelly, a visiting UC LEADS scholar from UC Irvine. Here I am, at UCSB, on a beautiful summer day, sitting in a computer lab, thinking about how to write this blog. It is difficult, as words are not exactly my strength.

What do I like about being here, people may ask? Well, actually, a lot of things. Here is a list of whatever I can think of at the moment:

- The beach is just about a 30-minute walk away. I can go there often without having to pay for parking nor public transportation. It also a good place to go to if one is stressed.
- The lagoon – I just like water in general. Also, there are snowy egrets and all sorts of birds I don’t see every day.
- It’s not that hot here. Currently, in August, it’s only 80F; meanwhile in Orange County (where I was born and raised), it’s normally 90F.
- It is summer; hence, there are not too many people here.
- Living in an apartment with other scholars – while this is normal for the typical college student, I am a commuter who has not had that opportunity yet. I have lived in the dorms in the past 2 summers though, but not an apartment.
- Free meal plans
- The people in my cohort
- My research group

Since I am a scholar, I should also mention my research interests. I am a math major, and my areas of interests include Algebra, Number Theory, and Combinatorics. At my home institution, I have conducted research in Algebra, so here, I want to try out Graph Theory.

Here at UCSB, I am working with Professor Padraic Bartlett and 2 other undergraduate students on how to break “almost-complete graphs” (that is, graphs such that every vertex is connected to almost every other vertex) into triangles. After 7 weeks of reading dense papers, drawing diagrams, counting, and mathematical thinking, we are able to prove this result. Now we are in the process of writing up our proof and revising it.

“That’s cool, but how can you apply this to the real world?” is a common question I, as a mathematician, get. Well, in general, if there seems like no immediate use, then there will be one eventually. That is how it worked with binary numbers, which were deemed “useless” until they were used in computer science. Though for my project specifically, breaking graphs into triangles can be applied to computer graphics.

As for my future research plans, I am not sure yet. I do like the topics given to me, but there might be more out there that will also capture my interest. I’m still currently exploring my mathematical interests.