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複素解析幾何セミナー
過去の記録 ～04/30｜次回の予定｜今後の予定 05/01～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
次回の予定
2026年05月11日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
日仏数学拠点FJ-LMIセミナーとの共同開催
Luc Pirio 氏 (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
https://forms.gle/8ERsVDLuKHwbVzm57
日仏数学拠点FJ-LMIセミナーとの共同開催
Luc Pirio 氏 (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
[ 講演概要 ]
Polylogarithms are special functions with many remarkable properties, notably their functional identities. The most interesting identities of this kind involve several variables and are known only in low weights. In weights 1 and 2, there is essentially one fundamental identity in each case: Cauchy’s equation for the logarithm and Abel’s five-term identity for the dilogarithm.
After introducing the subject, I will present natural generalizations, up to weight 6, of Cauchy’s and Abel’s identities. The new identities are no longer merely polylogarithmic, but hyperlogarithmic, and they arise naturally from the geometry of del Pezzo surfaces.
In the second part of the talk, I will discuss a generalization of an approach due to Gelfand and MacPherson in the weight 2 case, leading to a more canonical viewpoint on these hyperlogarithmic functional equations.
The first part of the talk is based on joint work with Ana-Maria Castravet.
[ 参考URL ]Polylogarithms are special functions with many remarkable properties, notably their functional identities. The most interesting identities of this kind involve several variables and are known only in low weights. In weights 1 and 2, there is essentially one fundamental identity in each case: Cauchy’s equation for the logarithm and Abel’s five-term identity for the dilogarithm.
After introducing the subject, I will present natural generalizations, up to weight 6, of Cauchy’s and Abel’s identities. The new identities are no longer merely polylogarithmic, but hyperlogarithmic, and they arise naturally from the geometry of del Pezzo surfaces.
In the second part of the talk, I will discuss a generalization of an approach due to Gelfand and MacPherson in the weight 2 case, leading to a more canonical viewpoint on these hyperlogarithmic functional equations.
The first part of the talk is based on joint work with Ana-Maria Castravet.
https://forms.gle/8ERsVDLuKHwbVzm57
