TexTAG Conference Report

Hi everyone. Sorry, but I’ve been at the Texas Undergraduate Geometry and Topology conference all weekend and I haven’t had time to write my blog post yet. I will post actual content as soon as I can, probably late tomorrow afternoon. In the meantime, I gave a talk on differential geometry at the conference! It’s not much of a consolation prize, but here are my slides from the talk.

Click to access TaleOfTwoArcLengths_animations_removed1.pdf

To better see the families of commensurate curves on various surfaces, we can animate our numerical integral as a function of the initial conditions. Here are some of the animations:

The Sphere

These curves are all just rotations of the sphere becuase the sphere is so symmetric!
Changing initial conditions for commensurate curves on the sphere.

The Paraboloid

Paraboloids are sphere like!
Commensurate Curve on a Paraboloid
Commensurate curve on the bottom of the paraboloid
Commensurate curve on the bottom of the paraboloid

The Hyperbolic Plane

Squiggles!
Commensurate curves on the hyperbolic plane

Okay. That’s all I have for now. If there’s demand, I’ll try and write more blog posts on geometry and describe this whole thing in a more accessible way.

 

2 thoughts on “TexTAG Conference Report

  1. Can you please write a blog post about this? I would love a more detailed explanation of what’s going on in these slides.

    1. Sure! But it might take a while. I’m a bit too excited about gravitational waves at the moment. 🙂

      (I’m also really busy.)

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