Short Talk: Aman Markar

Understanding the (near-)critical behaviour of Bernoulli percolation is a very challenging task. One case where things are slightly simpler is the high-dimensional case. It is expected that ,for $d>6$, the model should exhibit what is known as mean-field behaviour. This is something that is now well understood using a technique called lace expansion.   In this talk, I will present a new, more probabilistic approach to studying high-dimensional percolation. While this method currently gives weaker results than the lace expansion, it offers new insights and a different perspective on the problem. Based on joint work with Hugo Duminil-Copin, Romain Panis and Gordon Slade