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Alexander E Holroyd: Local Constraint Solving — How to Colour Without Looking (Much)

Time: Wed 2019-04-24 15.15 - 16.15

Location: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University 

Participating: Alexander E Holroyd (Seattle and Uppsala)

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Abstract: How can individuals cooperate to satisfy local constraints without a central authority? Individuals can make random choices and communicate with each other, but all must follow the same procedure. How small can we make the “coding radius” — the distance to which an individual must
communicate? In the setting of the integer line Z, there is a surprising universal answer that applies to every non-trivial constraint problem. In d-dimensional Euclidean space, answers are available for the
key case of proper colouring; it turns out that there is a huge difference between 3 and 4 colours. Finally, I'll mention how changing the question slightly has led to the discovery of an amazing
mathematical object that seemingly has no right to exist.