The Mathematical Institute and Oxford University Press announce the following colloquium:
Professor Kazuya Kato (University of Chicago)
Title: Heights of motives
Date and venue: 15 November, 4.30pm, Mathematical Institute
Abstract: the height of a rational number a/b (a,b integers which are coprime) is defined as max (|a|, |b|). A rational number with small (resp. big) height is a simple (resp. complicated) number. Though the notion height is so naive, height has played a fundamental role in number theory. There are important variants of this notion. In 1983, when Faltings proved the Mordell conjecture (a conjecture formulated in 1921), he first proved the Tate conjecture for abelian varieties (it was also a great conjecture) by defining heights of abelian varieties, and then deducing Mordell conjecture from this. The height of an abelian variety tells how complicated are the numbers we need to define the abelian variety. In this talk, after these initial explanations, I will explain that this height is generalised to heights of motives (a motive is a kind of generalisation of abelian variety.) This generalisation of height is related to open problems in number theory. If we can prove finiteness of the number of motives of bounded height, we can prove important conjectures in number theory such as general Tate conjecture and Mordell-Weil type conjectures in many cases.
Colloquia are followed by a reception designed to give people the opportunity to have more informal contact with the speaker. A book display will be available at this time in the common room. The series is funded, in part, through the generous support of Oxford University Press.
The colloquia are aimed towards a general mathematical audience.