9704424 Lawson This award is to provide partial support for a week long conference in gauge theory and low dimensional topology at Tulane University in the fall semester of 1997. The conference will be held in conjunction with the annual Clifford Lectures, given this year by Peter Kronheimer. Gauge theory has been the source of dramatic advances in low dimensional topology in recent years, and the work of Kronheimer and Tomasz Mrowka has been fundamental, particularly their settling of the Thom conjecture. A dozen other significant contributors to this area will give major talks, and additional shorter talks will round out the program. Despite the fact that we live in a universe of three spatial dimensions and one time dimension and have available all the intuition that this experience provides us, three and four dimensional objects have remained remarkably resistant to full understanding. In fact, mathematicians have found that in some respects higher dimensional spaces are more tractable, whereas some of the analytic tools available in higher dimensions cannot be used in dimensions three and four. This means that other methods that will apply in these so-called low dimensions are at a premium and is what makes so important the gauge theoretic methods first introduced by Simon Donaldson and more recently strikingly simplified by Nathan Seiberg and Edward Witten. ***
