BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dmitry Belyaev (Univ. Oxford\, UK) DTSTART:20200916T090000Z DTEND:20200916T094500Z DTSTAMP:20260421T173832Z UID:BPS/11 DESCRIPTION:Title: On the number of level sets of smooth Gaussian fields - I\nby Dmitry Bely aev (Univ. Oxford\, UK) as part of Bangalore Probability Seminar\n\n\nAbst ract\nLevel sets of smooth Gaussian fields appear in many areas of mathema tics. They have numerous applications outside of mathematics from astrophy sics to oceanology to biology. Probably the first significant progress in the study of level lines came in 1940s when Kac and Rice developed formula s that allow to compute the expected number of roots of a random function in 1d. These formulas can be generalised to higher dimension where they al low to compute the expected volume of level sets. Unfortunately\, these fo rmulas do not allow to study the number of level lines since it is a non-l ocal quantity which can not be written as a Kac-Rice-type integral formula . In this talk we will discuss recent progress in the study of the number of level lines for smooth Gaussian fields. \n\nIn the first part of the ta lk D. Belyaev will give a gentle introduction to the area and give a broad overview of recent results. In particular\, he will describe how the numb er of level lines depends on the level. This allows to show that the expec ted number of lines depends (almost) smoothly on the level and allows to g ive a low bound on the fluctuation of the number of level lines. In the se cond part S. Muirhead will explain in more details the ideas behind these results and will sketch the proof of the variance bound.The talk is based on a series of papers by D. Belyaev\, M. McAuley and S. Muirhead.\n LOCATION:https://researchseminars.org/talk/BPS/11/ END:VEVENT END:VCALENDAR