- 日時:2025年5月30日(金)16:50 — 17:50
- 場所:立命館大学 びわこくさつキャンパス ウェストウィング6階 談話会室 および Zoomミーティング
- 講演者:森下 昌紀(九州大学)
- タイトル:Arithmetic topology, Deninger’s foliated dynamical systems and Connes’ adele class spaces
- アブストラクト: Starting with a motivation in arithmetic topology, we explain firstly how Deninger’s foliated dynamical systems arise naturally from a fundamental question in number theory. Next, we explain C. Deninger’s striking program on the cohomological expression of number-theoretic zeta functions and intimate analogies between number rings and 3-dimensional foliated dynamical systems. We then introduce his conjecture on the regularized determinant expression of the Ruelle zeta function of a 3-dimensional foliated dynamical system in terms of leafwise cohomology. One of our results, which is joint with J. A. Alvarez Lopez and J. Kim, is a proof of this conjecture. It is based on the distributional dynamical Lefschetz trace formula due to Alvarez Lopez and Y. A. Kordyukov. Now there is a different approach of this zeta function issue, due to A. Connes, from noncommutative geometry, where the phase space is defined by the adele class space. Although the structures of foliation and dynamical system appear in both approaches by Deninger and Connes, their works seem deeply different and their relation has been unknown for a long time. Recently, I found a relation between Deninger’s arithmetic foliated dynamical system for Spec(Z) and Connes’ adele class space. This is my second result, which I will present in the seminar.
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https://ritsumei-ac-jp.zoom.us/meeting/register/7x_bhCFfRPSbiQPmln7bxA
連絡先:
野澤 啓
hnozawa[at]fc.ritsumei.ac.jp