Stick bombs

Nov 2022
talk fun craft

Summary:

Weave together 4 or 5 popsicle sticks in the right way, and you get a flat rigid pattern – until you drop it. The fast-released elastic energy shoots apart the popsicle sticks, producing a stick bomb. Join us as we try and discover the mathematics behind stick bombs, what makes them stay together and what makes them fall apart. Working together in groups, we’ll come up with Many of our own Cheerful Facts about tounge-depresser trajectiles :)

Presented at:

  • UC Berkeley Many cheerful facts, fall 2022

Stick bombs

The first week, I traced through this perspective on the simplest knot invariant, the linking number. I start from winding numbers in 2D, explained through flat connections on a line bundle. Extending to 3D, this gives gauss’s integral formula for linking numbers. Then I introduce the ableian chern-simons functional integral, and show that it formally computes linking numbers. Finally, I construct this as a topological quantum field theory, giving a way to compute linking numbers from knot diagrams.

The second week, This week, we will instead integrate over lie algebra-valued 1-forms (nonabeilain Chern Simons theory), and show that the resulting topological invariant is the jones polynomial. To do so, we introduce the axioms of topological quantum field theory, which gives a calculate the invariant by cutting up the manifold into small pieces. This shows us how our invariant changes when resolving a crossing in a knot, reproducing the skien relations of the Jones polynomial.

Here are some sources which I used for this talk.