Dynamical zeta functions, noncommutative geometry and arithmetic zeta functions

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Project objective

Research objectives and content The general theme in which I am interested are more or less hypothetical connections between (perhaps very generalized) dynamical systems and associated zeta functions on the one side and arithmetic zeta functions on the other side. Also the formalisms of my thesis were developed simultaneously for both kinds of zeta functions. First I want to improve some parts of my thesis in the more special situation of dynamical zeta functions. After that (which is a cut) I will try to improve results of Bost and Connes about C*-dynamical systems connected with arithmetic zeta functions. If there is time enough I also want to deal with a class of non-classical dynamical zeta functions introduced by Deninger and/or a new class of 'arithmetic' dynamical systems which I want to develop. Training content (objective, benefit and expected impact) As I was more occupied with arithmetic zeta functions during my time at Deninger's research group, I now want to study the side of dynamical systems more intensely. For this I want to learn the basic theory of classical dynamical systems and zeta functions (Ruelle zeta functions) as well as the fundamentals of noncommutative geometry for which the experts are at the IHES. I plan to emphasize this analytic side also in my future research. Links with industry / industrial relevance (22)

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Participants

• INSTITUT DES HAUTES ETUDES SCIENTIFIQUES · BURES-SUR-YVETTECoordinatorFrance

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