BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Maxim Kirsebom (University of Hamburg) DTSTART:20210315T161500Z DTEND:20210315T173000Z DTSTAMP:20260423T053139Z UID:NEDNT/17 DESCRIPTION:Title: T owards an extreme value law for the deepest cusp excursions of the unipote nt flow\nby Maxim Kirsebom (University of Hamburg) as part of New Engl and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr act\nThe unipotent flow on the unit tangent bundle of the modular surface is a classic example of a homogeneous flow when understood through the ide ntification with PSL_2(R)/PSL_2(Z). The ergodicity of the flow implies tha t almost every orbit is dense in the space and hence must eventually make excursions deeper and deeper into the cusp. We are interested in understan ding the nature of these excursions. In the described setting\, and more g enerally\, Athreya and Margulis proved that the maximal excursions obey th e logarithm law almost surely\, meaning that their growth rate scales the logarithm of the time. In this work we focus on a more precise description of this behaviour\, namely determining the probability that the deepest e xcursion fails to outperform the expected asymptotic behaviour by an addit ive amount. This question may be phrased in the language of extreme value statistics and we establish some results towards a complete extreme value law in this setting. The methods used are based on classical ideas from ge ometry of numbers. This is work in progress\, joint with Keivan Mallahi-Ka rai.\n LOCATION:https://researchseminars.org/talk/NEDNT/17/ END:VEVENT END:VCALENDAR