The mathematical work of H. Blaine Lawson, Jr.

Abstract

In this article, we celebrate the 80th birthday and remarkable career of H. Blaine Lawson, Jr. For more than half a century, Lawson has been a leading figure in mathematics. His work, a masterful combination of differential geometry, topology, algebraic geometry and analysis, has been enormously influential. He has made numerous fundamental contributions to diverse areas involving these subjects. He can be seen as a true “Renaissance man,” combining profound mathematical insight with a remarkable talent for expressing his discoveries with elegance and clarity. Roughly speaking, Lawson has changed the focus of his research every 10 to 15 years, in each instance, illuminating new fields of study with his unique insight and perspective. In the narrative that follows, we will endeavor, albeit with notable omissions, to showcase his most significant achievements. The order of presentation is essentially chronological. We will conclude with a concise overview of his highly influential expository work.