Combinatorics has experienced tremendous growth in the last century, and especially in the last few decades. This is in part due to the systematic study of the field that was initiated by many great mathematicians in the beginning of the 20th century. Additionally, the discovery of links between combinatorics and other fields of mathematics, such as algebra, analysis, logic, probability, and number theory, as well as various branches of computer science, showcased the importance of combinatorics and led to the development of an ever-growing toolbox containing methods from various fields. 

 

The focus of this workshop will be on extremal and probabilistic combinatorics which are particular strengths of the UK combinatorics community. The first area typically studies how large (or small) a parameter of a discrete collection of objects can be, provided it satisfies certain conditions, whereas the second seeks to describe typical properties of a discrete object drawn randomly from such a collection. Problems of both types arise naturally not only in combinatorics but also in other areas of mathematics and computer sciences.

 

Participants will work together in small groups on ambitious open problems, and there will additionally be a small number of research talks on the latest developments in the area.

 

The key objectives are to

• initiate and enhance collaborations involving UK combinatorialists, and

• generate internationally significant research outputs.
 

Alongside this, we also aim to

• give early career researchers a valuable opportunity for expanding their research interests and making lasting connections with more senior mathematicians, and

• celebrate and promote combinatorial research across the breadth of the UK.

 

Information on participation to follow in due course.