H2020Индивидуална стипендия2019–2021

LocalGlobal0Cycles · Local-global principles and zero-cycles

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2019-10-01 → 2021-09-30
Финансиране от ЕС: 174 167 €
Участници: 1
Схема: MSCA-IF

Линиите свързват координатора с партньорите.

Накратко на български

Нулевите цикли, които са обобщени рационални решения на системи от полиномни уравнения, се анализират чрез локално-глобални принципи. Това помага за разбирането на тяхното поведение и полага основи за нови изследователски посоки в геометрията и аритметиката.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Local-global principles and zero-cycles

The aim of the project was to use the theory of obstruction sets to investigate, through local-global considerations, both the quantitative and qualitative arithmetic behaviours of ``zero-cycles'', which can be viewed as generalised rational solutions to systems of polynomial equations. Whereas the theory of rational solutions to systems of polynomial equations is accessible from many perspectives (including analytic methods), the theory of zero-cycles seems to be much less accessible and requires a deeper geometric component. As a result, the arithmetic of zero-cycles is not nearly as studied as the arithmetic of rational points. Part of the motivation for the project was indeed to open up the area to a wider range of tools and to lay down the foundations for new research directions. Specifically, the researcher focused on the following four objectives, some of which have an open-ended, exploratory nature, due to the novelty of the research directions outlined: classification problems for zero-cycles; constructing new obstruction sets for zero-cycles; integral zero-cycles; arithmetic statistics of zero-cycles.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

The study of rational solutions to Diophantine equations is an important research area in number theory, with many concrete applications in different disciplines, including cryptography. The candidate's proposed work aims at investigating, via ""local-global"" techniques, the arithmetic behaviour of certain generalisations of rational solutions to Diophantine problems, called ""zero-cycles"". The goal is to systematically develop the theory of these generalised solutions in order to open it up to a wider range of tools and research directions, including arithmetic statistical ones (in the spirit of the work developed by Field medallist Prof Bhargava).The proposed supervisor, Prof Tim Browning, is a world-renowned expert in the study of Diophantine equations. He has considerable experience in successfully supervising research, having mentored several PhD students and postdoctoral researchers. The choice of IST Austria as the host institution is a natural one, given the perfect affinity of the supervisor and his number theory group's expertise to the candidate's proposed work.The candidate, Dr Francesca Balestrieri, completed her undergraduate studies at University of Cambridge and her graduate studies under an EPSRC Studentship at University of Oxford, where she obtained her DPhil in 2017. She is now a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. The candidate's proposed work on zero-cycles will be of great interest to the arithmetic geometry community, laying the foundations for new research directions and fruitful international collaborations. he project will better integrate her into the continental European research network and allow her to progress towards her career goal of becoming an established independent researcher at a leading European institution.""

Оригинален текст от CORDIS (на английски).

Участници

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA · KlosterneuburgКоординаторАвстрия