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.

Education

Costello was educated at the University of Cambridge where he was awarded a

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

in 2003 for research on

Gromov–Witten invariant In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic man ...

s supervised by

Ian Grojnowski Ian Grojnowski is a mathematician working at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. Awards and honours Grojnowski was the first recipient of the Fröhlich Prize of the London Mathematical So ...

Career and research

Costello works in the field of mathematical physics, particularly in the mathematical foundations of

perturbative In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for whi ...

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

and the applications of topological and

conformal Conformal may refer to: * Conformal (software), in ASIC Software * Conformal coating in electronics * Conformal cooling channel, in injection or blow moulding * Conformal field theory in physics, such as: ** Boundary conformal field theory ...

field theories to other areas of mathematics. In the book ''Renormalization and Effective Field Theory''Kevin Costello, ''Renormalization and Effective Field Theory'', Mathematical Surveys and Monographs Volume 170, American Mathematical Society, 2011, 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 In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex ...

for conformal field theories. Using this language, Costello gave a rigorous construction of the

Witten genus In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the ...

in elliptic cohomology, using a variant of

Chern–Simons theory The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and Jam ...

. Along with

Davide Gaiotto Davide Silvano Achille Gaiotto (born 11 March 1977) is an Italian mathematical physicist who deals with quantum field theories and string theory. He received the Gribov Medal in 2011 and the New Horizons in Physics Prize in 2013. Biography Gaiot ...

, 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 medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

ists Maxim Kontsevich and Edward Witten.

Publications

* Kevin Costello and Owen Gwilliam, ''Factorization Algebras in Quantum Field Theory'', Cambridge University Press, 2014

Awards and honours

Costello was elected a Fellow of the Royal Society (FRS) in 2018. He was awarded the

Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...

by the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

in 2017. In 2020 he was admitted as an honorary member of the

Royal Irish Academy The Royal Irish Academy (RIA; ga, Acadamh Ríoga na hÉireann), based in Dublin, is an academic body that promotes study in the sciences, humanities and social sciences. It is Ireland's premier List of Irish learned societies, learned socie ...

References

{{DEFAULTSORT:Costello, Kevin Year of birth missing (living people) Living people Irish mathematicians Alumni of the University of Cambridge Members of the Royal Irish Academy Northwestern University faculty