全学共通科目講義(1回生~4回生対象)
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現代の数学と数理解析 |
―― 基礎概念とその諸科学への広がり |
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第8回 | |
日時: | 2008年5月30日(金) 16:30-18:00 |
場所: | 数理解析研究所 420号室 |
講師: | HELMKE, Stefan 助教 |
題目: | CayleyとBacharachの定理 |
要約: |
A famous theorem of Blaise Pascal from 1640 says that
the three opposite sides of a hexagon inscribed in a conic meet
in collinear points. This was the first generalization of
Pappus' Theorem since more than 1200 years! It was partially
inspired by Kepler's observation, that the orbits of planets
are ellipses with the sun in one of their focal points. Pascal's
Theorem itself inspired a lot of new geometry. One of the
consequences was a wide generalization of his own theorem due to
Cayley, completed by Bacharach in 1881. Its proof is a fascinating
combination of geometry, topology, algebra and analysis. In my
talk, I will mainly concentrate on the developments in the
19th century, closely following a paper by D. Eisenbud, M. Green
and J. Harris.
Reference: |
"http://www.kurims.kyoto-u.ac.jp/ja/special-02.html" |