H2020Индивидуална стипендия2018–2020

HORUS · THE NON-ABELIAN HODGE THEORY OF AN ORBIFOLD KLEIN SURFACE

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

Период: 2018-09-01 → 2020-08-31
Финансиране от ЕС: 185 076 €
Участници: 1
Схема: MSCA-IF-EF-ST

Линиите свързват координатора с партньорите.

Накратко на български

Високата Тайхмюлер теория за специални геометрични обекти, наречени орбифолди, се изследва чрез нови математически методи. Това помага за по-доброто разбиране на топологията на сложни пространства и свойствата на реалните проективни триизмерни многообразия.

Този кратък обзор е генериран от изкуствен интелект

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

Резултати накратко

THE NON-ABELIAN HODGE THEORY OF AN ORBIFOLD KLEIN SURFACE

As developed by N. Hitchin, F. Labourie, V. Fock, A. Goncharov, O. Guichard and A. Wienhard, Higher Teichmüller Theory makes sense for fundamental groups of orientable surfaces. One specific goal of the theory is to construct discrete and faithful representations of such fundamental groups and to understand the topology of the Higher Teichmüller Spaces thus constructed. The main examples of Higher Teichmüller Spaces are Hitchin components and spaces of maximal representations, and a conjecture of Guichard, Labourie and Wienhard suggests that positive representations are also discrete and faithful. The main goal of the HORUS project was to develop Higher Teichmüller Theory for orbifold fundamental groups. Indeed, the classical Teichmüller theory of such groups is well understood, but their higher rank analogues have only been studied in rank 2, by S. Choi and W. Goldman. In collaboration with Daniele Alessandrini and Gye-Seon Lee, we studied orbifold Hitchin components in arbitrary rank. To do so, we extended Hitchin's Higgs bundles techniques to the orbifold case, in order to obtain an analytic parameterization of the Hitchin components in this case too. As an application, we constructed new examples of discrete and faithful projective representations of hyperbolic Coxeter groups. We also used our techniques to study the rigidity properties of real projective 3-manifolds.

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

Цел на проекта

For centuries, mathematical concepts have inspired technological progress. As the distance between fundamental research and applications shortens, the impact of mathematics on our everyday lives becomes stronger, and the long-standing European tradition of excellence in mathematical research reaffirms itself as a key factor of sustainable economic growth. In line with that tradition, the goal of the present project is to achieve and disseminate high-impact research results in the field of Differential Geometry, that will irrigate related disciplines, such as Theoretical Physics and, in the longer run, more applied fields. The applicant’s outstanding research record in Gauge Theory and Representations of Fuchsian Groups, combined with the expertise of his European hosts in the rapidly growing area known as Higher Teichmüller Theory, make the proposed collaboration between them unique, timely, and ideally shaped for success. The research results that they are setting out to obtain will redefine the field and open new lines of research. Moreover, the host institution is committed to providing high-quality training of the applicant at every step of the action, from concrete initiatives to reduce the gender gap in mathematical sciences to the use of technological tools for the dissemination and communication of research results. The completion of the present research project will thus bring a significant boost to the applicant’s career and establish the host institution as a pioneer in a new line of research, hereby strengthening its tradition of excellence and innovation. The project is in accordance with the recommendations of the 2016 consultation of the European Commission for Mathematics in Europe, according to which “the wealth of mathematical competence in Europe and its potential for European science and industry is undeniable”.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITE DE STRASBOURG · StrasbourgКоординаторФранция