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Introduction

Welcome to the blog I'll be keeping while participating in the 2018 Fields Undergraduate Summer Research Program. The program is through the Fields Institute for Research in Mathematical Sciences, which is on the campus of the University of Toronto in Ontario, Canada. I will be participating in Project 5 along with other students from around the world. From the above website:

"This project is about the methods used for numerical simulations of both exo-planetary systems and our own Solar System. Having fast and accurate numerical tools to perform such simulations is crucial if we want to understand the dynamical architecture of these systems."

My understanding of the project is as follows: we'll be working on a project that involves solving complicated equations (higher-order differential equations, specifically). These equations are complicated enough that we can't solve them using our nice standard techniques. Because of these complexities, we turn to finding a solution by numerical methods. Numerical methods work by approximating a solution based on certain information gathered about the function at certain points. The issue with approximating a solution, however, is that error is produced. This summer, we'll be looking at methods that will lessen the error associated with the current method of solving these particular equations. We'll be working with the "n-body problem," a variation of the "two-body problem."

Read about our project supervisor: Dr. Hanno Rein. 
Read more about the code behind this project: REBOUND

The program runs from July 3 to August 31, and over the course of these two months, I'll be documenting not only what I'm learning from the research program, but also what new experiences I'm having in Toronto.

I'm incredibly grateful for this opportunity and for everyone who helped make this possible for me, specifically my encouraging professors and mentors and my supportive friends. This summer will be so exciting, and I'm looking forward to sharing my experiences!

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Week 1 Update

I finally made it to Canada and just finished my first full week at the Fields Institute! St. George Street One of the campus dining halls Fields is housed on the University of Toronto's campus, and the participants of the program are given accommodations at one of the university's residence halls. Over the past week and a half, in addition to my research, I've been exploring the campus and neighborhood. I'm really enjoying getting to live in Toronto for the summer (especially because it's not as hot and humid as Atlanta right now)! Bloor Street West Thomas Fisher Rare Books Library As part of the research program, I have an office at the Fields Institute that I share with the two other members of my group the Project 8 group. Fields is great; for one, I don't think there are any whiteboards in the building - only blackboards.  There are also conferences and talks that are going on many of the days, so that means there's also free coffe...
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Update

Happy Tau ( τ)  Day! For those of you who may not be familiar with  τ , it's equivalent to 2 π , a constant extensively used in mathematics. I prefer   τ to  2 π because it's simpler (and because it's one number instead of two, so I'm less likely to make some sort of algebra or arithmetic mistake).  Read about some of the advantages of tau over pi here :  Let’s Use Tau—It’s Easier Than Pi . (Yes, that is a math book in my jacket pocket.  The wonders of pockets on men's jackets!) Now the update: I'm leaving for Toronto very soon, and the program at Fields starts on July 3rd. I don't have much more information on the research this summer, but our PI (principal investigator) sent an email with a few details. We'll be looking at hybrid symplectic integrators, which are numerical ODE (ordinary differential equation) solvers. I don't know much about them beyond that, but part of the goal for the research is to determine how they work and how...
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