SREACEP · Sparse Robust Expander with Applications in Combinatorial Embedding Problems
„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“
- Период
- 2018-01-01 → 2019-12-31
- Финансиране от ЕС
- 183 455 €
- Участници
- 1
- Схема
- MSCA-IF-EF-ST
Линиите свързват координатора с партньорите.
Накратко на български
Експандерите са специални мрежи от възли, които са едновременно пестеливи и силно свързани. Анализът на тяхната структура помага да се оцени колко устойчива е една мрежа при възникване на повреди.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Sparse Robust Expander with Applications in Combinatorial Embedding Problems
One of the major developments in combinatorics in the past four decades is that of expanders. It was first introduced to construct networks (represented by graphs) that are economical (sparse) and robust (highly connected). Expanders can be defined in various different ways. From the algebraic point of view, expanders are the graphs with large spectral gap; from the probabilistic point of view, random walks on expanders are rapidly mixing; and from the graph theoretic point of view, an expander is a graph whose vertex subsets have `large' boundaries. The main purpose of this project is to study expanders from the graph theoretic point of view through its expansion property, and investigate the interplay between expanders and two other central notions in modern combinatorics: Hamilton cycles and topological minors. The results and methods related to the cycle structure in a network (graph) can be adapted and used to evaluates the network's liability to deal with failures. Also, the techniques and methods learnt and developed during these projects opened new research directions. During the fellowship, the researcher explored some of these new directions.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
Expanders is a fundamental concept in combinatorics. From the application point of view, expanders have become a powerful tool in studying real life problems such as network design and error correcting codes. From the theoretical point of view, it is considered as a sparse analogue of Szemeredi's regularity (recognised by the 2012 Abel prize) with connections in algebra, analysis, geometry and topology.An exciting recent development has been the study of `sparse robust expanders' first introduced by Komlos and Szemeredi. Significant progress in several seemingly unrelated long-standing open problems has been established using techniques derived in this theory, including in work of Dr. Sharifzadeh. The proposed research aims to further develop this theory and derive a framework for solving embedding problems of combinatorial and topological nature. Tools developed here may find further applications that build bridges between combinatorics and other fields.The UK has been a leader in combinatorics and Warwick is one of the best in the UK with a combinatorics group of international reputation. The supervisor Professor Pikhurko is a world-leading expert in combinatorics. One of the focus of his projects funded by ERC and EPSRC is to study the expansion of graphs and groups with applications in analysis, which is closely related to this proposal. He is experienced in supervising postdocs and PhD students.Dr. Sharifzadeh obtained her PhD from the University of Illinois at Urbana-Champaign in Summer 2016. She has written 9 papers, 7 of which are published in leading international journals. In her work, she successfully applied combinatorial methods to resolve classical open problems in additive number theory, extremal combinatorics and topological graph theory. As an ambitious young researcher, she is determined to pursue an academic career. This proposal will integrate her into the European system and help her acquire the necessary skills to achieve her goals.
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITY OF WARWICK · COVENTRYКоординаторОбединеното кралство
Връзки
Данни: CORDIS, © Европейски съюз