I guess I'll be the first staff member to take the plunge

[Chris L T521]

Hey all,

My name is Christopher and I'm a second year Ph.D. student in mathematics at UC-Santa Cruz. I've been pursuing math since my sophomore year in high school because it was the only thing I was good at!

I guess people consider me as an introvert since I'm a pretty reserved and shy person. With my good friends, though, I'm pretty open and lax about things.

In my spare time (if it exists), I try to practice piano as much as I can (I've been playing for 14.5 years now), and I do some gaming. I also work on making notes for various topics in math (right now, I'm working on the differential equation notes for the tutorial, and some abstract algebra notes).

 

[Prove It]

Hey all,

My name is Christopher and I'm a second year Ph.D. student in mathematics at UC-Santa Cruz. I've been pursuing math since my sophomore year in high school because it was the only thing I was good at!

I guess people consider me as an introvert since I'm a pretty reserved and shy person. With my good friends, though, I'm pretty open and lax about things.

In my spare time (if it exists), I try to practice piano as much as I can (I've been playing for 14.5 years now), and I do some gaming. I also work on making notes for various topics in math (right now, I'm working on the differential equation notes for the tutorial, and some abstract algebra notes).

What are you writing your thesis about?

 

[Chris L T521]

What are you writing your thesis about?

It's still to be decided, but it will be related to dynamical properties of the four body problem.

 

[Prove It]

It's still to be decided, but it will be related to dynamical properties of the four body problem.

And for those of us with only a Bachelor's degree in mathematics, would you please explain what that is? lol

 

[Chris L T521]

And for those of us with only a Bachelor's degree in mathematics, would you please explain what that is? lol

Hey, I only have a Bachelor's degree too...and I'm still trying to make sense of this stuff.

So in short, I'm going to try to extend results obtained by my advisor in this paper. In his paper, he showed that for the zero-angular momentum three body problem with $1/r^2$ potential, the dynamics are equivalent to, modulo symmetries, a geodesic flow on the shape sphere minus three points -- or what he called a "pair of pants". The geodesic flow was generated by the Jacobi-Maupertuis metric, and in the case of equal masses, he showed the curvature was negative everywhere except two points (hence why the title is called "fitting hyperbolic pants to a three body problem").

My goal is to investigate what happens in the case of four bodies, and determine whether the J-M metric has negative curvature a.e. in this case. It may turn out that the problem will be phrased differently, but that's all I can provide you with for now. I hope this is satisfying to an extent! I never realized this stuff was so complicated, yet I was so intrigued by it.