AMPLE · A Study of the Notion of Ampleness in Model Theory and Tits Buildings
„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“
- Период
- 2019-09-01 → 2021-08-31
- Финансиране от ЕС
- 212 934 €
- Участници
- 1
- Схема
- MSCA-IF-EF-ST
Линиите свързват координатора с партньорите.
Накратко на български
Математическата логика и геометрията на сградите на Тиц се анализират, за да се открият връзки между тях чрез понятия като „амплитудност“. Това помага за разбирането на отворени хипотези в алгебрата и добавя ново направление за изследвания в теорията на моделите.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
A Study of the Notion of Ampleness in Model Theory and Tits Buildings
The project allocates in the area of Model Theory, which forms part of Mathematical Logic and has ample connections to surrounding fields of pure mathematics. The leading aim of the project was to establish new links between the area of Model Theory with Combinatorics and Algebra through a thorough study of the notions of Stationary Independence and Ampleness and use its implications to approach long standing open conjectures in the area, as well as to establish a novel interaction between Model Theory and Geometric Group Theory, or more precisely, the area of Tits Buildings. This is based on findings from the PhD thesis of the ER, where in joint work with her supervisor she was able to use methods from the area around Tits Buildings to resolve a long-standing open conjecture in Model Theory. Conversely, several important notions within buildings reflect abstract and well-studied objects in Model Theory. It hence seems that there is a strong connection between these two fields and exhibiting this clearly will change the area of Model Theory by adding a completely new field of research to it.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The proposed project AMPLE allocates in the area of mathematical Logic, Model Theory. It aims to develop a full understanding of the notion of ampleness and establish new connections between Model Theory and core mathematics.Model Theory aims to study and classify mathematical structures according to their THEORIES, that is, the class of all first order logic sentences that are true within them. One of the most important conjectures within Model Theory is Zilber's Trichotomy Conjecture, which suggested a classification of so-called strongly minimal structures - the building bricks of large classes of first order structures. Even though having been refuted quickly after its formulation, this conjecture and its counter example by Hrushovski have shaped the research in model theory and ultimately led Hrushovski to his outstanding proofs of the Mordell-Lang Conjecture, originating in the area of Number Theory. The notion of AMPLENESS was developed in order to classify the geometries left out in the Trichotomy Conjecture. Even though studied by many after its introduction, there is a plethora of open questions around this notion, witnessing that a thorough understanding is still missing. Answers to these questions have the potential to reshape the view on the classification of first order structures. The ER managed in her PhD thesis to solve one of the main open problems in this area, by combining tools from the field of TITS BUILDINGS, which was developed to classify simple algebraic groups and groups of Lie type. Together with the project Supervisor, who is a leading expert in the area of ampleness, the ER will establish a full understanding of the notion of ampleness, using its close connections to the theory of Tits Buildings. This project promises new bonds between Model Theory and core mathematics as well as a high applicability to longstanding questions within Model Theory itself. It is thus of high visibility and importance to the community.
Оригинален текст от CORDIS (на английски).
Участници
- IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE · LondonКоординаторОбединеното кралство
Връзки
Данни: CORDIS, © Европейски съюз