Codimension 2
From Mathematics
(→The dilogarithm) |
(→Motivation) |
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Not: <ref name="Hut13"/> but has an informative introduction... | Not: <ref name="Hut13"/> but has an informative introduction... | ||
| − | In the end of the 70's a beautiful story began, when mathematicians, with Bloch leading the way, began to discover a | + | In the end of the 70'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 | 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. | case of codimension 2 cycles, K_2, and the dilogarithm (this next polylogarithm after the usual logarithm) and quite explicit. | ||
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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 dilogarithm function which enters these relations in various ways. The dilogarithm became quite famous in many other areas of mathematics recently. Some of those application we want to discuss as well. For instance, the relation with zeta functions, the applications in physics, and in hyperbolic geometry (all of course not completely unrelated with each other). | 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 dilogarithm function which enters these relations in various ways. The dilogarithm became quite famous in many other areas of mathematics recently. Some of those application we want to discuss as well. For instance, the relation with zeta functions, the applications in physics, and in hyperbolic geometry (all of course not completely unrelated with each other). | ||
| − | Let me quote Zagier <ref name="Zag07"/>: | + | Let me quote Don Zagier <ref name="Zag07"/>: |
''Almost all of its ''[of the dilogarithm]'' appearances in mathematics, and almost all the formulas relating to it, have something of the fantastical in them, as if this function alone among all others possessed a sense of humor.'' | ''Almost all of its ''[of the dilogarithm]'' appearances in mathematics, and almost all the formulas relating to it, have something of the fantastical in them, as if this function alone among all others possessed a sense of humor.'' | ||
