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Christopher Deninger
Primes, knots and periodic orbits
17 janvier 2025 - 16:00Salle de conférences IRMA
In the 1960s Manin, Mazur and Mumford noted that from there was an intriguing analogy between prime numbers embedded into the spectrum of the integers and knots in 3-space. Later Kapranov, Reznikov, Morishita and other authors discovered further analogies between number rings and the topology of 3-manifolds. For example, the Iwasawa zeta function corresponds to the Alexander polynomial of a knot. The search for a cohomology theory related to the Riemann zeta function led to the discovery of analogies between number rings and a class of 3-dimensional dynamical systems, where the primes would correspond to the periodic orbits. For example, Riemann’s explicit formulas in analytic number theory correspond to a transversal index theorem in the dynamical context, proved by Álvarez-López, Kordyukov and Leichtnam. The dynamical systems analogy refines the previous analogy because forgetting its parametrization, a periodic orbit gives a knot. Recently, we have constructed foliated dynamical systems for number rings and even for all arithmetic schemes that have some but not yet all the expected properties. -
Patrick Massot
TBA
28 février 2025 - 16:00Salle de conférences IRMA
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Katharina Schratz
TBA
7 mars 2025 - 16:00Salle de conférences IRMA
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Eva Feichtner
TBA
25 avril 2025 - 16:00Salle de conférences IRMA