Kevin Costello's research concerns the mathematics of quantum field theory. Quantum field theory is one of the most widely used paradigms in physics, with applications ranging from the theory of fundamental particles to the study of exotic materials. Costello has made large parts of quantum field theory into rigorous mathematics, and uses modern mathematical techniques to provide new insight into physics.
Costello has contributed to a wide range of topics in mathematics related to quantum field theory, such as topological field theory, integrable systems, supergravity, elliptic genera, and holography.
He was awarded the Berwick prize of the London Mathematical Society in 2017, was an invited speaker at Strings in 2016, a Simons Fellowin 2012, an invited speaker at the ICM in 2010, and a Sloan Fellow in 2008.