Uniformly distributed sequences and covering of high-dimensional sets; a seminar by Anatoly Zhigljavsky

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The talk touches upon several topics from different subjects. First, I will talk about uniformly distributed sequences and different characteristics of uniformity. Second, I will argue that, contrarily to a wide-spread belief, the sequences with good space-filling properties do not resemble uniformly distributed sequences, especially if the dimension of the space is large. Most of the time I will spend on the problem of covering of a high-dimensional cube by n balls and will demonstrate several unexpected phenomena of good covering schemes. I will also mention the problem of quantisation also known as the problem of optimal facility location.