H2020Индивидуална стипендия2015–2017

KaMCAM · Kac-Moody groups and Computer Assistants in Mathematics

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

Период: 2015-08-01 → 2017-07-31
Финансиране от ЕС: 195 455 €
Участници: 1
Схема: MSCA-IF-EF-RI

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Накратко на български

Групите на Къртис-Тиц изследват симетрията на сложни геометрични обекти, докато софтуерните помощници анализират начина, по който се пишат математическите доказателства. Това помага за по-доброто описание на безкрайноразмерни структури и подобрява преподаването на концептуалното мислене при учениците.

Този кратък обзор е генериран от изкуствен интелект

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

Резултати накратко

Kac-Moody groups and Computer Assistants in Mathematics

The project addresses two distinct, yet interconnected work packages. 1) Curtis-Tits groups This work package falls within the realm of algebra, more precisely group theory. This is broadly speaking the study of symmetry of certain geometric and combinatorial objects. Curtis-Tits groups are generalizations of a class of groups of relevance to Theoretical Physics called Kac-Moody groups. Generally such groups are in some sense infinite dimensional. The purpose of the project is to completely classify and describe these groups In terms of a compact finite set of data and to study these groups and related geometric and combinatorial structures in terms of this data. We also wish to explore applications in various areas of mathematics and computer science. 2) Mathematical Research and Teaching with Proof Assistants The purpose of this work package was to address the well-known difficulties that students encounter when learning to write structured proofs, i.e. rigorous explanations of mathematical ore more generally formal logical statements. There exist many useful software packages for teaching and assessing computational aspects of mathematics. However, one of the major obstacles in teaching conceptual understanding and critical thinking skills within mathematics and sciences in general the fact that it is hard to produce and assess sufficient numbers of practice problems. There are so-called proof assistants, but these have been developed mainly for advanced computer science purposes and are unsuitable for students without advanced understanding of modern programming languages. Notably in the current computer age, computational skills are increasingly becoming irrelevant, whereas transferable skills coming from conceptual understanding are increasingly important.

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

Цел на проекта

This fellowship will enable the experienced Researcher Dr Rieuwert Blok - a currently USA-based European Union national - and Dr Corneliu Hoffman - as Host researcher based at the University of Birmingham - to carry out innovative and mutually beneficial research utilising their complementary skill sets. Blok brings extensive research experience in buildings, Lie theory and geometries while Hoffman's background is in group theory, representation theory and number theory. The fellowship aims to create optimal conditions for the Researcher to reintegrate into ERA for the benefit of both the Researcher and the ERA.The action comprises two distinct, yet interconnected Work Packages . The first one concerns Curtis-Tits groups, a large family of groups recently introduced by the Researcher and Dr Hoffman.This family includes groups of established importance, namely groups of Lie and Kac-Moody type, but in fact contains many new groups of great theoretical significance and practical interest.The action develops methods that open up this promising family for further study. It then determines key properties such as simplicity, and explores and establishes applications in geometric group theory, combinatorics, group presentations, and computer science. The subject area is an innovative blend of group theory, homological algebra, topology, geometry, number theory and computer science. The second package is an interdisciplinary project between mathematics and computer science, exploring the promise of effectively using the recent developments surrounding proof assistants in teaching and research. It builds forth upon pioneering work in this direction by both researchers at their respective universities.

Оригинален текст от CORDIS (на английски).

Участници

THE UNIVERSITY OF BIRMINGHAM · BirminghamКоординаторОбединеното кралство