"Random walks and critical percolation" Gordon Slade, University of British Columbia The talk will survey recent developments that prove precise estimates showing subdiffusive behaviour for random walks on three structures related to critical percolation:

(i)

the invasion percolation cluster on a tree,

(ii)

the incipient infinite cluster for oriented percolation in spatial dimensions above four,

(iii)

the incipient infinite cluster for percolation on Z^d for d > 6.

In all three cases, the results rely on a general theorem for random walk on a random graph, in which hypotheses on volume growth and effective resistance of the random graphs imply conclusions about the behaviour of the random walk