Kevin Costello

from Wikipedia, the free encyclopedia
Kevin Costello

Kevin Costello (* 1977 in Cork , Ireland ) is an Irish mathematician and mathematical physicist .

Costello received his PhD in 2003 from Ian Grojnowski at Cambridge University (Gromov-Witten Invariants and Symmetric Products). He is Professor of Mathematics at Northwestern University and, since 2014, Professor of Theoretical Physics at the Perimeter Institute in one of the two chairs donated by the Krembil Foundation (the other was given to Davide Gaiotto ).

Costello deals with topological quantum field theories and their connection with Yang-Mills theories and their supersymmetric variants. He succeeded in a strictly mathematical description of the renormalization group flow in quantum field theories (introduced by Kenneth Wilson ), in the context of which he also gave a new alternative proof of the renormalization of pure Yang-Mills theories. In his treatment of gauge theories he uses the Batalin-Vilkovisky formalism.

He was also able to establish a connection between exactly solvable lattice models in two dimensions (such as the Ising model of statistical mechanics , formally via the Yang-Baxter equation with spectral parameters) and four-dimensional quantum field theories. These are topological quantum field theories ( Chern-Simons theory ) in which one of the three real dimensions has been complexified (the theory is holomorphic in one dimension, topological in two dimensions).

With his mathematical definition of quantum field theories he gave a strict justification of the Witten sex (a multiplicative sex constructed by Witten using methods of quantum field theory ) a compact complex manifold .

In 2017 Costello received the Berwick Prize and in 2018 he was elected to the Royal Society . For 2020 he was awarded the Leonard Eisenbud Prize for Mathematics and Physics.

Fonts

  • Renormalization and Effective Field Theory. In: Mathematical Surveys and Monographs. Volume 170, American Mathematical Society, 2011, Preprint
  • A geometric construction of the Witten genus. I, Arxiv Preprint 2010 , Part 2, Arxiv
  • Topological conformal field theories and gauge theories. In: Geometry & Topology. Volume 11, 2007, pp. 1539-1579, Arxiv
  • Topological conformal field theories and Calabi-Yau categories. In: Adv. Math. Volume 210, 2007, pp. 165-214, Arxiv
  • with Owen Gwilliam: Factorization algebras in quantum field theory. Cambridge University Press, preprint
  • with Claudia Scheimbauer: Lectures on mathematical aspects of (twisted) supersymmetric gauge theories. Les Houches Winter School 2012, Arxiv
  • Supersymmetric gauge theory and the Yangian. Arxiv, 2013

Web links

Individual evidence

  1. ↑ Kevin Costello in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ A philanthropic organization in Toronto that until then had primarily promoted medical research
  3. ↑ That was one of the achievements of Gerardus' t Hooft and Martinus Veltman in the early 1970s, for which they received the Nobel Prize in Physics . At that time they also proved the renormalizability of Yang-Mills theories with spontaneous symmetry breaking , as is required in the Standard Model .
  4. ^ Integrable lattice models from four-dimensional field theories.
  5. ↑ The work was recognized by Edward Witten as the solution to a problem for which he had been looking for a long time. Witten, Interview with Hirosi Ooguri, Notices AMS, May 2015, p. 491
personal data
SURNAME Costello, Kevin
BRIEF DESCRIPTION Irish mathematician
DATE OF BIRTH 1977
PLACE OF BIRTH Cork