Professor of Mathematics
Mathematics has been called the “Queen of the Sciences” because it is the language that reveals and describes the laws governing the physical world. As such, Notre Dame is dedicated to its flourishing at all levels, whether it is being studied by first-year students as part of the University’s Core Curriculum or developed in novel ways by the research of faculty, graduate students, and advanced undergraduates.
My research is in the area of mathematics known as geometric analysis. Many physical phenomena, from the spread of fire to the motion of stars, can be described in purely geometric terms. But the equations one encounters, even when considering something as simple as the soap bubbles made by children at play, are incredibly complex.
These nonlinear partial differential equations, as they are called, are ubiquitous in mathematical applications to the physical, social, and even life sciences. Remarkably, the same equations that describe soap bubbles also arise when studying black holes in cosmology. Although mathematicians have made great advances in understanding these equations in the last century, many basic questions remain beyond the reach of our current techniques.
I work closely with the geometry and topology group in our mathematics department, which includes several world-class researchers. We are excited about the University’s decision to continue investing in the strength of the group through the Strategic Faculty Hiring Initiative, a commitment that will allow us to expand our expertise to an exciting area at the intersection of mathematics and physics known as quantum field theory.