Valuation theory and series methods in o-minimal fields

Název projektu anglicky
Valuation theory and series methods in o-minimal fields
Anotace anglicky
O-minimal fields are mathematical structures generalizing the real closed field of reals, making for a suitable setting for studying tame geometric problems using model theory and providing a common generalization to semialgebraic and sub-analytic real geometry. The project will advance the knowledge of the valuation theory of o-minimal fields with a T-convex valuation, with focus on those defining exponentiation. The main planned contributions concern elementary λ-spherical completions for uncountable cardinals λ. In particular in regard of their expansion by a T-derivation, their structural descriptions in term of generalized power-series, their application to geometric problems, and the study of some new invariants for said completion operation. This will provide new tools to further broaden the scope of application of o-minimality, which already has numerous successful applications throughout mathematics. The interaction with generalized power series will have on the side an algebraic study of formal summability of these series with links to commutative algebra and topology.

Kategorie VaV
ZV - Základní výzkum
OECD FORD - hlavní obor
10101 - Pure mathematics
OECD FORD - vedlejší obor
—
OECD FORD - další vedlejší obor
—
CEP - odpovídající obory <br>(dle <a href="http://www.vyzkum.cz/storage/att/E6EF7938F0E854BAE520AC119FB22E8D/Prevodnik_oboru_Frascati.pdf">převodníku</a>)
BA - Obecná matematika

Důvěrnost údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Systémové označení dodávky dat
CEP26-GA0-GN-R
Datum dodání záznamu
4. 5. 2026

Podobné projekty(10)