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Seminar on Geometric Complex Analysis
Seminar information archive ～05/02｜Next seminar｜Future seminars 05/03～
| Date, time & place | Monday 10:30 - 12:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Next seminar
2026/05/11
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI seminar
Luc Pirio (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
https://forms.gle/8ERsVDLuKHwbVzm57
Joint with FJ-LMI seminar
Luc Pirio (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
[ Abstract ]
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.
[ Reference 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
