Uniformly distributed sequences and covering of high-dimensional sets; a seminar by Anatoly Zhigljavsky
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![Uniformly distributed sequences and covering of high-dimensional sets](https://cardiff.imgix.net/__data/assets/image/0010/1746073/Uniformly-distributed-sequences-and-covering-of-high-dimensional-sets-2020-1-13-8-48-20.jpeg?w=570&h=321&fit=crop&q=80&auto=format )
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.
21-23 Senghennydd Road
Cathays
Cardiff
CF24 4AG