会议介绍

Networks are part of our modern life. Transport and computer networks are examples of physical networks that we use everyday; social networks such as Facebook are instances of nonmaterial networks. Roughly, a network, or a graph as is called in mathematics, is a set of objects together with a set of links each joining two objects. It is remarkable that this simple concept captures features of many systems from a variety of domains in mathematics and beyond. The mathematics subject underlying the theory of networks is graph theory, which is a young but rapidly maturing area of increasing importance. Apart from its wide applications in many different domains (e.g. computer science, information theory, combinatorial optimization, and so on), graph theory is a fascinating subject of pure mathematics that has deep connections with many other areas, including group theory, topology, random walks, probability theory, mathematical physics, to name just a few.

In many application domains, it is essential to construct networks that are optimal in terms of some given measure. For example, a network design problem that has enormous impact to many fields is to construct families of Ramanujan graphs, which are sparse but extremely well connected graphs with increasing orders. This challenging problem has attracted many top mathematicians in the world including several ICM plenary and invited speakers. Another important problem that attracted many mathematicians and computer scientists is the one of finding the largest order of networks with a given maximum degree and diameter and construct such networks whenever possible. It turns out that this innocent-looking problem is quite challenging, and its study involves a range of techniques in graph theory, group theory, spectral theory of graphs, and topology.

To promote research on optimal network topologies, an international workshop in the area, IWONT, was set up nearly ten years ago. This is a medium-size workshop that attracted many leading researchers worldwide. So far six editions of IWONT were held in six different countries. We plan to organize the next edition of this well established workshop, IWONT 2016, at Tsinghua Sanya International Mathematics Forum, Sanya, Hainan Provice, China. The purpose of this workshop is to provide an excellent forum for leading mathematicians in the area of optimal network topologies to exchange their ideas, communicate the latest results and develop further collaborations. We plan to invited up to 15 Chinese participants to attend IWONT 2016. Thus this workshop will also provide an excellent opportunity for Chinese mathematicians (especially young researchers) to abreast latest progress in the area and develop collaborations with overseas participants. Topics of the workshop include but are not limited to: degree-diameter problem; cages; connectivity and reliability of networks; cycles and factors in graphs; construction techniques for large graphs and digraphs; structural properties of large graphs and digraphs; spectral techniques in graph theory; network design problems from communication.

We expect that after the workshop all participants will have a better understanding of the state-of-the-arts of the area and will have gained impetus to further investigate important problems in the area as well as new problems that will certainly come out of the workshop. (We plan to organize a problem session as recommended by TSIMF.)

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