H2020Индивидуална стипендия2017–2019

CombLimit · Limit Theory in Combinatorics

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

Период: 2017-03-01 → 2019-02-28
Финансиране от ЕС: 134 239 €
Участници: 1
Схема: MSCA-IF-EF-ST

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Накратко на български

Математическите графи анализират големи мрежи, като например социалните връзки или комуникационните системи, чрез техните граници при безкраен размер. Развиването на тази теория помага за по-доброто разбиране на света около нас.

Този кратък обзор е генериран от изкуствен интелект

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

Резултати накратко

Limit Theory in Combinatorics

Large networks are present everywhere is our world. We have communication networks, traffic networks, social networks, we use our network of brain cells, etc. Graphs are the mathematical abstraction of networks. Properties of large graphs are analyzed by their limit when the size tends to infinity. This is analogous to how a physical medium is defined as a continuous object describing the case when the number of particles tends to infinity. This is a very recent area of mathematics and the goal is to contribute to its general mathematical theory. This will lead to a better understanding of our world.

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

Цел на проекта

Graph limit theory is a new and important field, motivated by large real-life networks such as the internet, the nervous system, traffic networks, social networks, interaction graphs of proteins, etc. Sparse graph limit theory is a direction partially inspired by these applications. This is a new and intensively studied field, and one of the two main topics of the research proposed. Local algorithms or constant-time distributed algorithms is an important tool for sparse graph limit theory, and this is in the focus of the proposed research. It is also useful to understand stochastic processes and phase transitions in large networks, and it is strongly related to ergodic theory.The applicant very recently demonstrated through some examples that the tools of limit theory can be very useful in solving combinatorial problems as well. This observation opened the door for plenty of new applications, which are also in the focus of the proposed research.With the proposed CombLimit initiative the applicant would complement the research agenda of the Rényi Institute, and he would also be an important link connecting pure mathematics with its applications in computer science, economics, physics and biology. Upon completion of the CombLimit MSCA program, the applicant will have a good basis for successfully applying a tenured/permanent position at Rényi Institute.

Оригинален текст от CORDIS (на английски).

Участници

HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET · BudapestКоординаторУнгария