BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Samantha Fairchild (University of Washington) DTSTART:20201002T161500Z DTEND:20201002T173000Z DTSTAMP:20260423T021433Z UID:NEDNT/3 DESCRIPTION:Title: Co unting social interactions for discrete subsets of the plane\nby Saman tha Fairchild (University of Washington) as part of New England Dynamics a nd Number Theory Seminar\n\n\nAbstract\nGiven a discrete subset V in the p lane\, how many points would you expect there to be in a ball of radius 10 0? What if the radius is 10\,000? Due to the results of Fairchild and fort hcoming work with Burrin\, when V arises as orbits of non-uniform lattice subgroups of SL(2\,R)\, we can understand asymptotic growth rate with erro r terms of the number of points in V for a broad family of sets. A crucial aspect of these arguments and similar arguments is understanding how to c ount pairs of saddle connections with certain properties determining the i nteractions between them\, like having a fixed determinant or having anoth er point in V nearby. We will focus on a concrete case used to state the t heorem and highlight the proof strategy. We will also discuss some ongoing work and ideas which advertise the generality and strength of this argume nt.\n LOCATION:https://researchseminars.org/talk/NEDNT/3/ END:VEVENT END:VCALENDAR