Kevin Joseph Costello FRS is an Irish mathematician, since 2014 the Krembil Foundation's

William Rowan Hamilton Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathema ...

chair of theoretical physics at the Perimeter Institute in

Waterloo, Ontario Waterloo is a city in the Canadian province of Ontario. It is one of three cities in the Regional Municipality of Waterloo (formerly Waterloo County, Ontario, Waterloo County). Waterloo is situated about west-southwest of Toronto, but it is n ...

, Canada.

Education

Costello was educated at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

where he was awarded a

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 2003 for research on Gromov–Witten invariants supervised by Ian Grojnowski.

Career and research

Costello works in the field of

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

, 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 which ...

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

and the applications of

topological Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, wit ...

and conformal 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 In theoretical physics, the renormalization group (RG) is a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying p ...

flow formalism of Kenneth Wilson and proved the renormalizability of

Yang–Mills theory Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special un ...

in this framework. More recent work on formalism for quantum field theory uses the idea of a

factorization algebra In mathematics and mathematical physics, a factorization algebra is an algebraic structure first introduced by Beilinson and Drinfel'd in an algebro-geometric setting as a reformulation of chiral algebras, and also studied in a more general s ...

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 r ...

elliptic cohomology In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology. It is related to elliptic curves and modular forms. History and motivation Historically, elliptic cohomology arose from the study of elliptic genera. I ...

, using a variant of

Chern–Simons theory The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and James Harris Simons, who intr ...

. 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 Gai ...

, 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 Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

ists

Maxim Kontsevich Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He ...

and

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...

Publications

* Kevin Costello and Owen Gwilliam, ''Factorization Algebras in Quantum Field Theory: volume 1'', Cambridge University Press, 2017 ISBN 1-107-16310-2 * Kevin Costello and Owen Gwilliam, ''Factorization Algebras in Quantum Field Theory: volume 2'', Cambridge University Press, 2021 ISBN 1-107-16315-3 * Kevin Costello, Renormalization and Effective Field Theory, Mathematical Surveys and Monographs 170, American Mathematical Society, 2022 ISBN 978-1-4704-7008-1

Awards and honours

Costello was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

(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 society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

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

Royal Irish Academy The Royal Irish Academy (RIA; ), based in Dublin, is an academic body that promotes study in the natural sciences, arts, literature, and social sciences. It is Ireland's premier List of Irish learned societies, learned society and one of its le ...

References

{{DEFAULTSORT:Costello, Kevin Year of birth missing (living people) Living people 21st-century Irish mathematicians Alumni of the University of Cambridge Members of the Royal Irish Academy Northwestern University faculty Place of birth missing (living people)