Abstract:

The counterpart to algebraic geometry over the complex numbers is real algebraic geometry over the reals. Here semialgebraic sets are considered, i.e. sets that are defined by finitely many equalities and inequalities of real polynomials. As algebaic geometry can  be done over arbitrary algebraically closed fields, real algebraic geometry can be performed over arbitrary real closed fields.

So far a good measure and integration theory for semialgebraic sets and functions over arbitrary real closed fields was missing. We establish in this general setting a full Lebesgue measure and integration theory such that the main results from the classical one including Stoekes' theorem hold. The construction involves methods from model theory, real anlaytic geometry, o-minimal geometry, valuation theory and the theory of ordered abelian groups.

We use our Lebesgue integration to define new invariants of motivic style for affine varieties over the reals or real analytic functions. For this purpose we work with the field of real Puiseux series as arc space.

Tee/Kaffee/Gebäck

ab  16:45 Uhr,

Arnimallee 3,  Raum 006

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Koordinator:  Prof. Dr. Alexander Schmitt

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