Nationality Irish Fields Mathematics | Role Mathematician Name Kevin Costello Doctoral advisor Ian Grojnowski | |
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Institutions Northwestern University
Perimeter Institute Thesis Higher Genus Gromov–Witten Invariants as Genus Zero Invariants of Symmetric Products (2003) Known for Mathematical theory of renormalization
Topological quantum field theory Books Renormalization and Effective Field Theory, The Court of Admiralty of Ireland, 1575-1893 Institution Northwestern University, Perimeter Institute for Theoretical Physics | ||
Alma mater University of Cambridge | ||
Kevin costello supersymmetric gauge theory and derived geometry lecture 1
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.
Contents
- Kevin costello supersymmetric gauge theory and derived geometry lecture 1
- Kevin costello supersymmetric gauge theory and derived geometry lecture 3
- Work
- Books
- References
Kevin costello supersymmetric gauge theory and derived geometry lecture 3
Work
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.