BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ariyan Javenpeykar (Johannes Gutenburg Universität) DTSTART:20210409T170000Z DTEND:20210409T183000Z DTSTAMP:20260423T040335Z UID:CAGS/9 DESCRIPTION:Title: On the conjectures of Campana\, Lang\, and Vojta\nby Ariyan Javenpeykar ( Johannes Gutenburg Universität) as part of Columbia algebraic geometry se minar\n\n\nAbstract\nWhy do some polynomial equations have only finitely m any solutions in the integers? Lang-Vojta's conjecture provides a conjectu ral answer and relates this number-theoretic question to complex geometry. I will start out this talk explaining the Lang-Vojta conjectures and prov ide a survey of currently known results. I will then present two new resul ts:\n\n1. If a projective variety has only finitely many rational points o ver every number field\, then it has only finitely many birational automor phisms. (Joint with Junyi Xie.)\n\n2. If a projective variety X is a ramif ied cover of an abelian variety A over a number field K with A(K) dense\, then the complement of (the image of ) X(K) in A(K) is still dense. (Joint with Pietro Corvaja\, Julian Lawrence Demeio\, Davide Lombardo\, and Umbe rto Zannier.)\n\nThese results are motivated by the Lang-Vojta conjectures (I will explain how)\, and also provide evidence for these conjectures.\n \nI will then move on to Lang-Vojta's conjectures over function fields in characteristic zero and explain how to verify a version of Lang-Vojta's co njecture for the moduli space of canonically polarized varieties (joint wi th Ruiran Sun and Kang Zuo). If time permits\, I will discuss the conjectu re "opposite" to Lang\, as formulated by Campana\, and some recent progres s here (joint with Erwan Rousseau).\n LOCATION:https://researchseminars.org/talk/CAGS/9/ END:VEVENT END:VCALENDAR