Probabilistic methods have proved to be an invaluable tool in Combinatorics, and have led to major progress in recent years. As an illustration of this, I will discuss several examples in the area of design theory and graph decompositions. Here the aim is to split a large object into many suitable small ones. Classical results in this area have often been limited to symmetric structures, as these allow for the exploitation of these symmetries or the use of algebraic techniques. Probabilistic approaches had a huge impact on the area recently. They allow for the construction of designs/decompositions in more complex or general settings, and have led to the solution of a number of longstanding problems.
Professor Kühn is the Mason Professor in Mathematics at Birmingham University. Her research interests are Extremal and Probabilistic Combinatorics. Professor Kühn has received several research grants, including an ERC Starting Grant. She has been awarded the European Prize in Combinatorics in 2003 and the Whitehead Prize by the London Mathematical Society in 2014. Further recognition for her research includes an invited lecture at the International Congress of Mathematicians in 2014.
Further information about Professor Kühn’s work can be found on her website