Title: Symmetries of manifolds

Abstract: We outline some questions involving symmetries of 3- and 4-dimensional manifolds and explain the application of these ideas to different problems in low-dimensional topology. We will see that symmetries of manifolds play an unexpected role in the study of such fundamental topics as exotic phenomena (which measure the difference between smooth and continuous topology) and sliceness obstructions for knots (that is, whether a knot bounds a smoothly embedded disk in the four-dimensional ball).