|Alma mater||University of Cambridge|
|Thesis||Higher Genus Gromov–Witten Invariants as Genus Zero Invariants of Symmetric Products (2003)|
|Doctoral advisor||Ian Grojnowski|
|Known for||Mathematical theory of renormalization
Topological quantum field theory
Kevin Costello is an Irish mathematician, currently the Wayne and Elizabeth Jones Professor of Mathematics at Northwestern University. Since 2014, Costello is holding the Krembil Foundation William Rowan Hamilton chair of theoretical physics at the Perimeter Institute.
Kevin Costello works in the field of mathematical physics, particularly in the mathematical foundations of perturbative quantum field theory and the applications of topological and conformal field theories to other areas of mathematics. In the book Renormalization and Effective Field Theory he introduced a rigorous mathematical formalism for the renormalization group flow formalism of Kenneth Wilson and proved the renormalizability of Yang-Mills theory in this framework.
More recent work on formalism for quantum field theory uses the idea of a factorization algebra to describe the local structure of quantum observables, such as the operator product expansion for conformal field theories. Using this language, Costello gave a rigorous construction of the Witten genus in elliptic cohomology, using a variant of Chern-Simons theory. Along with Davide Gaiotto, Kevin Costello was one of two researchers appointed to named chairs by the Perimeter Institute in 2014, funded by a $4 million investment by the Krembil Foundation. Costello's appointment was praised by Fields medalists Maxim Kontsevich and Edward Witten.
- Kevin Costello, Renormalization and Effective Field Theory, Mathematical Surveys and Monographs Volume 170, American Mathematical Society, 2011, ISBN 978-0-8218-5288-0
- Kevin Costello and Owen Gwilliam, Factorization Algebras in Quantum Field Theory, Cambridge University Press, 2014
- Kevin Costello and Tucker Costello, Game Theory and Squirrels: Chasing Uncatchable Solutions, Nicol Press (Independent), 2019 (forthcoming)
- "Perimeter Institute and Krembil Foundation Partner to Recruit World-Leading Physicists | Perimeter Institute". Perimeterinstitute.ca. 2013-11-16. Retrieved 2014-05-07.
- Costello, Kevin J. (2010). "A geometric construction of the Witten genus, I". arXiv: [math.QA].
- "Waterloo think tank gets even smarter". The Globe and Mail. 2013-11-16. Retrieved 2014-05-07.