Luca Capogna Receives Five-Year Grant to Use Mathematics to Classify and Understand the Nature of Shapes

September 26, 2018

Luca CapognaLuca Capogna, professor and head of the Department of Mathematical Sciences, has received a five-year, $42,000 grant from the Simons Foundation, a 24-year-old organization that funds research into mathematics and the sciences. The project being funded is titled “Topics in Nonlinear PDE and in Quasiconformal Mappings.”

The goal of Capogna’s research is to classify all possible shapes—whether the curls of a lettuce leaf shape or the space swept up by a robot arm as it moves through all of its possible configurations—using a mix of geometry and analysis methods. By better classifying and understanding shapes, scientists will better understand their nature and how they behave.

The research should enable Capogna to determine whether or not two spaces are similar. For instance, two shapes may look very different but have hidden similarities, from a mathematical perspective.

Capogna’s project, which is a continuation of research he’s been conducting for the past 10 years, could ultimately be applied to the study of cloud computing or even social networks. For instance, he is using mathematical models that relate to curved spaces, such as a curling lettuce leaf, to understand spaces that expand very quickly, a technique that connects a leaf that takes up more space as it uncurls to a cloud of data or a social network that rapidly expand in size.

Award Date: July 31, 2018