Mathfest days 1-2: talks

I’ll post slides and give a blurb about what i got out of the talk.

The first talk dealt with uncertainty; some of it was human reaction to it, some of it was the various types of noise (yes, not all noise is purely random; white, pink and..brown noise?)   This would have been a good talk to have heard before teaching time series.

Its relation to music was brought up. And yes, noise can actually enhance stability!

Next was the first part of a series of 3 talks.

The first part: given an analytic function where $f(0) = 0, f'(0) = \lambda$ is there a change of coordinates that turns this into a linear function?  Answer: yes, if $|\lambda| \neq 1, |\lambda| \neq 0$. But if $|\lambda| = 1$ the fun starts. One can rule out lambda being a root of unity. But that is where is gets complicated.

Next came a talk on game theory and Nash equilibriums.

this slide shows a funny “paradox”.  The spring shows one thing. Now look at the diagram in the lower right hand corner. Imagine having 100 cars at S trying to get to T. Upper route: second route takes 1 hour; first route is total number of cars on that route divided by 100 hours.  Lower route: just the opposite (1 hour first leg, total no of cars divided by 100 hours for the second route. Now if cars were just assigned 50 top, 50 bottom, then every driver takes 1.5 hours, period.

Now put in a zero time route from the top to the bottom (one way). Each car in the top can reduce its time by taking that short cut.  but if ALL of them do…then each of them would EVENTUALLY take 1.5 hours as before, (because all of them take this short cut hoping to avoid their 1 hour leg) but the bottom saps are now saddled with a 2 hour leg..so overall, opening this made things WORSE for everyone.

Cryptography talk: in the “tree image”, there is a cat there; you can barely make it out by tilting your screen.

The above are from some of the other talks; there is quite a bit of math there.

We also had a “geometry of check number” talk and a talk about encryption ..and yes…you can use a linear regression principle to encrypt.  Think about the message being a perfect regression line, and the encryption being the adding of errors. If you are working in the real numbers, a least square fit gives the message. Now use this principle with, say, a different field.

Day two: second lecture: about curves …complex curves which are really surfaces.

Can you identify a polynomial, say, $z^2 + c$ by the closure of its periodic and preperiodic (finite orbit) points?  If you superimpose the Julia sets, you do get overlap but they might not correspond to common periodic points.

Ok, a bit of topology and symplectic geometry. The latter is interesting stuff; here you worry about volume invariants.

Yes, I’ve studied two of these objects in detail

Author: oldgote

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