Codimension 2
From Mathematics
(→The dilogarithm) |
(→Introduction) |
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Not: <ref name="Hut13"/> but has an informative introduction... | Not: <ref name="Hut13"/> but has an informative introduction... | ||
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| + | In the end of the 70's a beautiful story began, when mathematicians, with 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 later triggered an enormous amount of research and was the motivation for many modern 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 conjecture, ... | ||
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| + | 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 beyound the | ||
| + | relations between line bundles, codimension 1 cycles (divisors), invertible functions and the logarithm that everybody knows well. | ||
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| + | While the first half of the seminar focuses on the explicit relation between (algebraic) K_2, the second (algebraic) Chern class of vector bundles and codimension 2 cycles the second half is devoted to the dilogaritm which enters these relations in various ways. It became quite famous in many other areas of mathematics recently and some of those application we want to discuss as for example the applications in physics and for volumes of hyperbolic spaces. | ||
| + | Let me quote Zagier <ref name="Zag91"/>: | ||
= Schedule = | = Schedule = | ||
