BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jennifer Park (Ohio State University) DTSTART:20250513T190000Z DTEND:20250513T200000Z DTSTAMP:20260423T130411Z UID:MITNT/116 DESCRIPTION:Title: The Quadratic Manin-Peyre conjecture for del Pezzo surfaces\nby Jennif er Park (Ohio State University) as part of MIT number theory seminar\n\nLe cture held in Room 4-149 in the Mclaurin Buildings (building 4).\n\nAbstra ct\nManin-Peyre conjecture\, counting point of bounded height on Fano vari eties\, has been the subject of intense research in the past few decades. We provide a general framework for the Manin-Peyre conjecture for the symm etric square of any del Pezzo surface X\, and prove the conjecture for the infinite family of nonsplit quadric surfaces. Previously\, there were onl y two examples in the literature: Sym^2(P^2) and Sym^2(P^1 x P^1). In orde r to achieve the predicted asymptotic\, we show that a type II thin set o f a new flavour must be removed. A key tool we develop and that can be app lied to further examples is a result for summing multiplicative functions and Euler products over quadratic extensions. To establish our counting re sult for the specific family of quadric surfaces\, we improve existing lat tice point counting results in the literature and make crucial use of a no vel form of lattice point counting. This work is joint with Francesca Bale strieri\, Kevin Destagnol\, Julian Lyczak\, and Nick Rome.\n LOCATION:https://researchseminars.org/talk/MITNT/116/ END:VEVENT END:VCALENDAR