[geometry-ml:05454] 連続講義(Sabbah, Yu)

[Takuro Mochizuki]

皆様

先日お伝えしましたClaude SabbahさんとJeng-Daw Yuさんの連続講義についてですが、
詳細が決まりましたのでご案内申し上げます。
https://www.kurims.kyoto-u.ac.jp/en/seminar/seminar-takuro2.html
変更がある場合はホームページにてお知らせいたします。

このメールを重複して受け取られた際はご容赦ください。

望月拓郎

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講演者: Claude Sabbah, Jeng-Daw Yu
タイトル: Bessel and Airy moments: arithmetic, periods and Hodge theory
日程: 1. 1月29日 14:00--16:00
      2. 1月30日 10:00--12:00
      3. 1月30日 14:00--16:00
      4. 1月31日 10:00--12:00 
場所: 数理解析研究所本館111号室
アブストラクト (全4回):

1. General introduction (C. Sabbah)
After presenting the general framework envisioned by the physicists Broadhurst and Roberts concerning the moments of Kloosterman sums, we will summarize the known results within their program and the methods that lead to such results. We will also consider moments of cubic sums, for which similar arithmetic results are less advanced. We will finally emphasize open questions.

2. Arithmetic (J.-D. Yu)
The main arithmetic result is the proof of a functional equation for the modified L-function attached to moments of Kloosterman sums. The objective of this talk is to explain the methods that enable one to make use of a theorem of Patrikis and Taylor in the theory of automorphic forms. It relies on the analysis of a pure motive attached to a toric hypersurface acted on by a finite group.

3. Exponential Hodge theory (C. Sabbah)
Broadhurst and Roberts computed experimentally Hodge numbers related to some symmetric powers of Bessel differential equations and conjectured a general formula for these numbers. One of the main question was to construct a pure motive that would produce these numbers. We will explain how the exponential Hodge theory of Kontsevich and Soibelman makes easier such a computation and how it can be adapted to the case of symmetric powers of Airy differential equations, where irregular Hodge numbers appear.

4. Periods (J.-D. Yu)
Physicists have been working with integrals and sums that are related by an underlying motive. Bessel and Airy moments are periods attached to a motive related to moments of Kloosterman and cubic sums. These periods satisfy quadratic relations that can be made more explicit by using an exponential motive rather than a classical motive. For moments of Kloosterman sums, this method enables us to check that a conjectural formula of Broadhurst and Roberts for the critical values of the L-function is in accordance with a general conjecture by Deligne.