## Symmetry Groups at Science Unlimited

I gave a talk about symmetry groups at Science Unlimited 2019.

The slides are available here, for the curious.

## MSLC Summer Seminar

- May 30th “Derivation and applications of the gamma function” by David Salwinski
- June 6th “An Extension of Heron’s Formula” by Zohreh Shahbazi
- June 13th “What is Homology?” by Parker Glynn-Adey
- June 20th “Exploring Mathematics Learning Support Across Canadian Universities” by Rubina Shaik and Shrijan Rajkarnikar
- June 27th “Liouville numbers and irrationality measure” by David Salwinski
- July 4th “Representation theory” by Lisa Jeffery
- July 11th “Geodesics on Surfaces of Revolution” by Amanda Petcu
- July 18th “An (informal) Introduction to Model Theory and Skolem’s Paradox.” by Yasin Mobassir
- July 25th “Geometric Reflections” by Parker Glynn-Adey
- August 1st “The Inscribed Square Problem” by Amanda Petcu

## Geometric Reflections

There is something pleasing to a mystic in such a land of mirrors. For a mystic is one who holds that two worlds are better than one. In the highest sense, indeed, all thought is reflection — Chesterton

## Hyperbolic Visualizations!

Thanks to Vi Hart, Andrea Hawksley, Elisabetta A. Matsumoto, and Henry Segerman for making these amazing things!

## The Quantum Gravity Topological Quantum Field Theory Blues by Scott Carter

Scott Carter has some poetry up on his website. He works on knotted surfaces, and I think this version is just great. Back in the day, I wanted to understand knotted surfaces and I remember looking at his work a bit.

I’ve been calculating

I said I’ve been calculating

calculating all night long

Got a quasi- triangular Hopf algebra

and I wrote down the coproduct wrong.I’ve been integrating

integrating the whole day through

I said I’ve been integrating

integrating the whole day through

Got a Chern-Simons functional integral

and its convergent, too.I’ve been writing down knot diagrams

converting them to braids

Using the Alexander isotopy

you know I’m not afraid

I’ve been

assigning modules

to each of these six strings

been doin’ it for weeks now

and I still don’t understand a thing.I’ve got them old Quantum Gravity

Topological Quantum Field Theory Blues

I’ve got them old Quantum Gravity

Topological Quantum Field Theory Blues

And without NSF funding I think that you would, too.

## Science Rendezvous!

This year, at Science Rendezvous, we shared symmetry and geometry. These areas of math are very beautiful and full of lovely patterns. In particular, we focused on how to connect geometry and symmetry using group theory. This approach was pioneered by Donald Coxeter, one of the most famous mathematicians of the twentieth century, and former professor at the University of Toronto. The big theme of our display was the notion of symmetry groups. This talk Symmetry and Groups by Professor Raymond Flood of Gresham College gives a great introduction to this connection.

Lukas brought his kaleidoscope, and I got it on video!

## Three-Dimensional Kaleidoscope

My highschool student, Lukas Boelling, made this three-dimensional icosahedral/dodecahedral kaleidoscope with his dad, @eric_boelling. Lukas based his models off this excellent paper: Alice through Looking Glass after Looking Glass: The Mathematics of Mirrors and Kaleidoscopes by Roe Goodman. Stay tuned for more models!

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