Title:
Playing dodgeball with normality
Abstract:
Normal numbers have had an important place in elementary
number theory and have got various and serious connections/implications
with effective computability theory and algorithmic information theory
(in theoretical computer science). In this talk we talk of various
results/conjecture related to normal numbers and discuss the proof of
an important theorem of Wolfgang Schmidt on normal numbers, which
basically says that one can construct a real number which dodges
normality with respect to any subset S of natural numbers while being
normal with respect to another subset R of natural numbers, if R and S
satisfy certain consistency criterion (this criterion is the most basic
one).