An invitation to probabilistic group theory

Speaker: Professor Tim Burness

Venue: Room 210, Haina Building 2, Zijingang Campus

Abstract: Many problems in mathematics involve determining the existence (or otherwise) of an element (or elements) in a set with special properties. In some cases, existence may be established through a direct construction, but this can often turn out to be very difficult. Non-constructive methods are designed to overcome these difficulties, often leading to short and elegant proofs.

In this talk, we will introduce the application of probabilistic techniques in group theory, which is a special type of non-constructive method that has been successfully applied to resolve a wide range of challenging problems in recent years. We will discuss the origins of these ideas, which can be traced all the way back to the gambling dens of 18th century Paris, and we will highlight some of the exciting recent breakthroughs at the research frontier. This talk will be accessible to all mathematicians.