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Exponential periods and o-minimality

Dr. Johan Commelin

Friday, 2020-11-27 10:30

In this talk I will present on joint work with Philipp Habegger and Annette Huber. Let α ∈ ℂ be an exponential period. We show that the real and imaginary part of α are up to signs volumes of sets definable in the o-minimal structure generated by ℚ, the real exponential function and sin|_[0,1]. This is a weaker analogue of the precise characterisation of ordinary periods as numbers whose real and imaginary part are up to signs volumes of ℚ-semialgebraic sets; and it points to a relation between the theory of periods and o-minimal structures.

Furthermore, we compare the definition of naive exponential periods to the existing definitions of cohomological exponential periods and periods of exponential Nori motives and show that they all lead to the same notion.