Sailing to criterion sets for quadratic forms

Název projektu anglicky
Sailing to criterion sets for quadratic forms
Anotace anglicky
Number fields, quadratic forms, and continued fractions are among the most classical and prominent objects of study in number theory. In this project, we will discover and establish novel connections between the arithmetic of number fields and the geometry of generalized continued fractions. Specifically, this will involve relating universal quadratic forms and their criterion sets, additively indecomposable integers in totally real number fields, and sails of lattices in R^n. Championed by our team, the last decade saw remarkable progress on these topics over real quadratic fields, i.e., the case n=2, and some promising, but sporadic results in higher degrees. Our principal goal is to uncover a deeper theory connecting sails, indecomposables, and criterion sets. As applications of our new theory, we aim at significant breakthroughs on Arnold's conjectures related to realizability for sails, Kitaoka’s conjecture on ranks of universal quadratic forms, and the broad hypothesis that criterion sets are not as big and incomprehensible as expected so far.

Kategorie VaV
ZV - Základní výzkum
OECD FORD - hlavní obor
10101 - Pure mathematics
OECD FORD - vedlejší obor
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OECD FORD - další vedlejší obor
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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-GA-R
Datum dodání záznamu
27. 4. 2026

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