# Pure Maths Colloquium: Sophie Stevens

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: | Lecture Theatre C |

When: | Nov 14 2019 @ 16.00 |

Video: | Not recorded |

Speaker: | Sophie Stevens University of Bristol |

Title: | Distinct distances in the plane |

Between any pair of points lying in a plane over any field we can define a distance quantity. If we have a finite number of points, we then have a finite number if distances. The question I would like to talk about is: how many distances must occur between any set of points?

This question was originally asked by ErdÃ¶s and, up to a logarithmic factor, resolved over the reals by Guth and Katz in 2010; I will discuss how the question can be approached over general fields. This is work joint with B. Murphy and M. Rudnev.