# 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)

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.

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.