In 1984, K. Mahler published a paper entitled "Some suggestions for
further research", in which he writes the following moving statement: "At
the age of 80 I cannot expect to do much more mathematics. I may however,
state a number of questions where perhaps further research might lead to
interesting results." One of these questions was regarding intrinsic
approximation on the Cantor set. In Mahler's words, "how close can
irrational elements of Cantor's set be approximated by rational numbers in
Cantor's set"? In this talk, I will describe recent advances towards
answering Mahler's question on fractals in general and on the Cantor set in
particular. The talk is intended for a general audience and no prior
knowledge on fractal geometry nor Diophantine approximation will be
assumed.
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Last modified: April 11 2016 - 18:14:43