This summer I’m doing my first SURF! It’s a math SURF, and my mentor studies low dimensonal topology, specificallyHeegaard Floer homology.
I’m working on the SURF with another undergrad, so we’ll be working
together to complete different parts of the project. Our main project is to write a
program to compute Heegaard Floer correction terms from a variety of
input methods. For the first few weeks, I’ll be working on several of
the input methods, including getting input from a drawing of a link.
A quick summary: A knot in math is basically the kind of
knot you tie, except that the ends of the knot are connected so there’s
no loose ends. Here’s a picture of a trefoil knot:
Trefoil knot drawn by Knotilus
A link is what you get when you have multiple knots linked together, like the Borromean rings here:
Borromean rings drawn by Knotilus
alternating link is a link with a diagram such that if you start
anywhere on the link and follow the strand you're on, the crossings
alternate over, under, over, under, etc. or under, over, under, over,
etc. The trefoil knot and Borromean rings are both alternating.
One input method for my SURF project is to take an alternating link
projection, shade regions of the link, and then use the shaded regions
and intersections to create a graph (the kind with nodes and edges). For
example, the program Plink
lets a person draw a link with their mouse. Part of the algorithm is
then to load the drawing and shade regions (while keeping track of
them), like in the picture below.
Link drawn in Plink (left) and shaded regions (right)
Based on the shaded regions and intersections, a graph and quadratic form can be calculated for each link projection. The quadratic form can then be used to calculate the Heegaard Floer correction terms.
Since I'm doing a math SURF, I don't have to go to a lab or anywhere specific on campus to work on the project. Although the view from my dorm room is very nice, it can get lonely in the morning since most people are at labs or JPL. So for the first day, I decided to go work in Annenberg (the computer science building), since they have an undergraduate computer lab.
View from my summer dorm room (the blurriness is from the window screen)
For some of the other inputing methods for the SURF project, I'll first have to learn more about
topology and read a little about homology. My list of topics to learn about include plumbed 3-manifolds, Seifert fibered rational
homology spheres, and Dehn surgery. Fortunately I know several other math majors staying at Caltech over the summer!
This summer I had the incredible opportunity to do a 10-week internship at Gilead Sciences in Foster City, CA. For those unfamiliar, Gilead Sciences, Inc. is a research-based biopharmaceutical company focused on the discovery, development, and commercialization of innovative medicines.
With 45 Nobel Laureates on its Faculty Roster, it’s not surprising that research is an integral part of the Caltech undergraduate experience. One of the programs that promotes such research is the Summer Undergraduate Research Fellowship (SURF). There is no minimum knowledge or experience required to participate in a Caltech SURF. In fact, students can participate in a SURF as soon as the summer after their freshman year. It is not difficult to get a SURF. All you need to do is find a mentor who is working in an area of research that interests you and willing to mentor you through a research project. The mentor can work in a Caltech lab, at the NASA Jet Propulsion Laboratory (JPL), or at another participating institution. Once you find a mentor, you work together to write a project proposal that you later send to the SURF office for review and approval. About 98% of the SURF proposals get approved. This fellowship is a great way to explore various fields of research and obtain real, hands-on experience where you get to apply the theoretical knowledge you’ve learned in class. Not only do you get to work and learn alongside your mentor, but you also get compensated for your time. The length of the SURF is ten weeks, and it starts at the beginning of the summer. However, it is not uncommon for many students at Caltech to continue their research project throughout the academic school year.
Like many students at Caltech, I suffer from a slight boba addiction, where side effects may include over caffeination, minor sugar highs, and of course, a large toll on one’s wallet. This addiction is not helped by the fact that there are at least three boba shops within walking distance of campus. So, after an entire term’s worth of boba runs, I came back from winter break with a new year’s epiphany: it was time to get a job. Rather than try to curb my addiction, I decided to find a way to subsidize it.
Research at Caltech looks different for every student, and can often vary term by term. As a chemistry major, my course requirements are on the lighter side for a Caltech major, and many chemistry majors take advantage of the lighter course load to join research groups. This can be whenever the student wants, but many people join labs during their freshman or sophomore years. Some may work in one lab only, and some may switch between labs during the course of their undergraduate studies, depending on if their interests change.