David Seifert, St John’s College
Sometimes a problem is too complicated to be solved directly but can be broken down into simpler subproblems. One can hope that by solving these subproblems, perhaps repeatedly, one approaches a solution of the original problem. The “method of alternating projections” allows us to do just that in a wide range of situations, from trying to divide a length of string into three equal pieces to solving Poisson’s equation on moderately unpleasant domains. I shall discuss a few of these applications of the method of alternating projections and present some of the main aspects of the underlying theory. If there is time I may also discuss how the problem becomes more interesting as we pass from finite to infinite dimensional spaces.