Title: Height functions for motives, Hodge analogues, and Nevanlinna analogues Speaker: 加藤和也 (Kazuya Kato, University of Chicago) Time: 2017-9-27, 16:30-17:30 Place: N913 Abstract: We compare height functions for (1) points of an algebraic variety over a number field, (2) motives over a number field, (3) variations of Hodge structure with log degeneration on a projective smooth curve over the complex number field, (4) horizontal maps from the complex plane C to a toroidal partial compactification of the period domain. Usual Nevanlinna theory uses height functions for (5) holomorphic maps f from C to a compactification of an agebraic variety V and considers how often the values of f lie outside V. Vojta compares (1) and (5). In (4), V is replaced by a period domain. The comparisons of (1)--(4) provide many new questions to study. Attachment: