Annette Huber-Klawitter: Exponential periods and o-minimality

Oberseminar, Oct. 15, 2020

(joint work with Johan Commelin and Philipp Habegger)

Roughly, period numbers are defined by integrals of the form $\int_\sigma\omega$ with $\omega$ and $\sigma$ of algebraic nature. This can be made precise in very different languages: as values of the period pairing between de Rham cohomology and singular homology of algebraic varieties or motives defined over number fields, or more naively as volumes of semi-algebraic sets.

More recently, exponential periods have come into focus. Roughly, they are of the form $\int_\sigma e^{-f}\omega$ with $\sigma,\omega$ and now also $f$ of algebraic nature. They appear as periods for the Rham complex of an irregular connection. We want to explain how the “naive” side of the story can be formulated in this case.