# Pure Maths Colloquium: Nicolai Haydn

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: | Jun 18 2019 @ 16.00 |

Video: | Not recorded |

Speaker: | Nicolai Haydn University of Southern California |

Title: | Entry and Return Times Distributions in Dynamical Systems |

We consider maps with invariant measures and look at the time it takes for random points to enter a given (positive measure) set. For return times a theorem of Kac states that on average the return times are the reciprocal of the size of the return set. The actual return times however have a distribution which typically allows for arbitrarily long returns. We want to consider a sequence of shrinking sets that contract to a single point or, possibly, to some more complicated zero measure set. With good control over the shrinking target sets one can prove meaningful limiting results which tend to be either a straight Poisson distribution or a compound Poisson distribution.