# Applications of non-commutative harmonic analysis

### From Santa Fe Institute Events Wiki

This would be a shortened version of the 4-hour tutorial I am preparing for a conference (topics). Let me know if you are interested.

Non-commutative harmonic analysis is based on group representation theory, but I do not expect people to have prior knowledge about that. Only familiarity with linear algebra is assumed.

The tutorial will answer the following questions:

1. What is the natural generalization of Fourier analysis to groups?

2. What does the Fourier spectrum of functions on permutations look like and what is the interpretation of the individual components?

3. How do non-commutative FFTs work?

4. How can we use all this stuff for multi-object tracking?

5. What is the bispectrum and why do we love it so much?

6. How can we construct simultaneously translation and rotation invariant features for images?

7. How can we tell in polynomial time whether two graphs are the same or not? (OK, still working on that one)

Risi.

I'd definitely be interested if my head hasn't exploded by then. --James

yup - john

i'm in for sure - mike

I'm in. -Kristen

yeah cool! Will L.

I would really like to participate, but I can't do it Friday June 15. Can we perhaps switch to any other day? Thanks a lot -Alex Shpunt