next seminar: UNUSUAL DAY AND TIME 5 MAY 17:00 MSK/16:00 EUR

[Alexander Shen]

Next meeting of the seminar will happen in unusual day/time: Tuesday 5
may 16:00 Paris time / 17:00 Moscow time

LINES AND POINTS (discussion)

An effective dimension of a point in a plane is the liminf of the
Kolmogorov complexity of its $2^{-n}$ approximations divided by $n$. The
dimension of a line is defined similary (lines are dual to points). It
turns out that if a line has dimension d<1, then its points have all
dimension in the interval [d,d+1], and for d>=1 the interval is [1,2].
Trying to understand this result, I thought that it would be instructive
to consider the finite case (of lines and points over a finite field
with $2^n$ elements - there is another finite version, with
approximations to reals, but this is another story). Indeed, Don Stull
(who will come to the meeting, I hope) managed to prove the first part
(for lines of small complexity), whilt the second case remains open
(AFAIK). We will try to discuss his argument (starting with simpler
result about the maximal complexity of line points)


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