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Summer 2016: Codimension 2

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  • Seminar
When Apr 18, 2016 02:00 PM to
Jul 23, 2016 04:00 PM
Where 404
Contact Name Fritz Hörmann
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In the 1970's a beautiful story began, when mathematicians, with Spencer Bloch leading the way, began to discover a beautiful connection between algebraic K-Theory, algebraic cycles and polylogarithms. The first work was restricted to the case of codimension 2 cycles, K_2, and the dilogarithm (this next polylogarithm after the usual logarithm) and quite explicit. This story, for the next 35 years until now, triggered an enormous amount of research and was one of the motivations for many modern (and quite abstract) developments and conjectures, as for example the theory of higher algebraic K-Theory (Quillen), mixed motives (Voevodsky - the ideas going back to Grothendieck), motivic cohomology, Bloch-Kato conjectures, Beilinson conjectures ...

The intention of this seminar is to study the beginnings of this subject as they evolved historically. The hope is that people might appreciate and understand better many of the recent developments in the field when they have some "easy" explicit examples in mind that go just a little bit beyond the relations between line bundles, codimension 1 cycles (divisors), invertible functions and the logarithm that everybody knows well. (Nevertheless the latter will be rediscussed in the first three talks).

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