Rolla: day one morning

I am in Rolla for a mathematics conference. I swam 3100 yards this morning; 1000 warm up, 10 x 100 on the 1:45 (last one was 1:40, others 36-39), 10 x 100 (fly/free/back/free) on 2.

There was one other swimmer who was slightly faster than I; that helped.

Update I understood very little of the first talk; was it point set topology or general? Ok, I know what “perfectly normal” is (seperation axiom T 3.5) and I figured out what was meant by the space [0,1] x {-,+} in the interval topology, but that was about it.

Note on this space: one can view this set with this topology in a couple of ways. If one looks at the unit square in the plane and then looks at the two segments {(x,0), x between 0 and 1 inclusive} and, {(x,1), x between zero and 1 inclusive} and declares a set to be open if there is an open set in [0,1] x [0,1] which intersects BOTH segments that produces this set, or equivalently, one can use a lexographic order topology with – being lower than + in the second coordinate.

The second talk (about hyperbolic group theory) was a bit more understandable.

Lunch update I went to John Milnor’s talk on the Mandelbrot set (this is the set of points in the complex plane that do NOT go to infinity under the map f(z) = z^2 + c for some “c”. He pointed out that there is a sequence of regions (if you go to the reference, check out the almost disklike regions) that converge to a set; it is unknown if these things converge to a unique point.

Image from the site “The Area of the Mandelbrot set” (recommended)

John Milnor won the Field’s Medal in 1962 (mathematical equivalent of the Nobel Prize) and is frequently mentioned in the book A Beautiful Mind.

We ate Chinese food for lunch (“we” being Denise and Mat; two of my math friends) and I’ll have to make time to walk a bit in the evening.

Update Lunch was too heavy; I am sleepy. None of these talks are really in my area (topology of 3-manifolds, especially knot theory) though at least the dynamical systems talks have nice photos and one can get the gist of what is going on.

In a nutshell: dynamical systems is the study of sets of points that arise from taking certain kinds of maps from one space to itself and iterating the map over and over again. The last talk dealt with taking equivalence classes of “types” of sets that can be obtained in such a manner (say, closed loops), looking at “sequences” of such sets (finite, possibly) and putting a topology on such sequences in a way that helps one understand those sets themselves.

These sets are subsets of the so-called Julia sets, which are, roughly speaking, the sets of points that don’t exhibit stable behavior under repeated map iteration.

The Fatou set is the complement of the Julia set. (these are the “stable” types of points)


March 29, 2007 - Posted by | mathematics, swimming, travel, Uncategorized

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