Kevin Costello

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Kevin Costello

Kevin Costello Royal Society.jpg
Kevin Costello at the Royal Society admissions day in London, July 2018
Kevin Joseph Costello

Cork, Ireland
Alma materUniversity of Cambridge (PhD)
Known forRenormalization
Topological quantum field theory
AwardsBerwick Prize (2017)[1]
Scientific career
InstitutionsNorthwestern University
Perimeter Institute
ThesisGromov–Witten invariants and symmetric products (2003)
Doctoral advisorIan Grojnowski[2]

Kevin Joseph Costello FRS is an Irish mathematician, since 2014 the Krembil Foundation's William Rowan Hamilton chair of theoretical physics at the Perimeter Institute in Waterloo, Ontario, Canada.[1][3]


Costello was educated at the University of Cambridge where he was awarded a PhD in 2003[4] for research on Gromov–Witten invariants supervised by Ian Grojnowski.[2]

Career and research[edit]

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[5] 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.[6] 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.[3][7]


  • Kevin Costello and Owen Gwilliam, Factorization Algebras in Quantum Field Theory, Cambridge University Press, 2014[ISBN missing]

Awards and honours[edit]

Costello was elected a Fellow of the Royal Society (FRS) in 2018.[8] He was awarded the Berwick Prize by the London Mathematical Society in 2017.[1]


  1. ^ a b c "Kevin Costello – Perimeter Institute".
  2. ^ a b Kevin Costello at the Mathematics Genealogy Project
  3. ^ a b "Perimeter Institute and Krembil Foundation Partner to Recruit World-Leading Physicists | Perimeter Institute". 2013-11-16. Retrieved 2014-05-07.
  4. ^ Costello, Kevin Joseph (2003). Gromov-Witten invariants and symmetric products. (PhD thesis). University of Cambridge. OCLC 894595138. EThOS
  5. ^ Kevin Costello, Renormalization and Effective Field Theory, Mathematical Surveys and Monographs Volume 170, American Mathematical Society, 2011, ISBN 978-0-8218-5288-0
  6. ^ Costello, Kevin Joseph (2010). "A geometric construction of the Witten genus, I". arXiv:1006.5422 [math.QA].
  7. ^ "Waterloo think tank gets even smarter". The Globe and Mail. 2013-11-16. Retrieved 2014-05-07.
  8. ^ "Kevin Costello".

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