Kevin Costello

Research Interests

My research uses tools from mathematics to explore string theory and quantum field theory. The long-term goal of my research is to provide rigorous constructions of (parts of) string theory with a view towards formulating string dualities in mathematical terms. My current focus is on twisted forms of the AdS/CFT correspondence and on the formulation of integrable systems in string and gauge theory.

Awards

• Honorary member of the Royal Irish Academy
• Eisenbud prize for mathematical physics, American Mathematical Society
• Fellow of the Royal Society
• Berwick Prize of the London Mathematical Society

Recent Publications

• The Chern-Simons Origin of Superstring Integrability, Kevin Costello, Bogdan Stefański jr , 2005.03064
• Boundary Chiral Algebras and Holomorphic Twists, Kevin Costello, Tudor Dimofte, Davide Gaiotto 2005.00083
• Twisted Supergravity and Koszul Duality: A case study in AdS3, Kevin Costello and Natalie Paquette 2001.02177
• Hyperbolic String Vertices, Kevin Costello, Barton Zwiebach , 1909.00033
• Gauge theory and integrability III, Kevin Costello and Masahito Yamazaki, 1908.02289
• Anomaly cancellation in the topological string, Kevin Costello and Si Li, 1905.0926
• Twisted holography, Kevin Costello and Davide Gaiotto, 1812.09257
• Higgs and Coulomb branches from vertex operator algebras, Kevin Costello, Thomas Creutzig and Davide Gaiotto 1811.03958
• Unification of integrability in supersymmetric gauge theories, Kevin Costello and Junya Yagi 1810.01970
• Vertex operators and 3d N=4 gauge theories, Kevin Costello and Davide Gaiotto, 1804.06460
• Gauge theory and integrability, II. Kevin Costello, Masahito Yamazaki and Edward Witten, 1802.01579
• Gauge theory and integrability, I. Kevin Costello, Masahito Yamazaki and Edward Witten, 1709.09993
• Topological Chern-Simons/Matter theories, Mina Aganagic, Kevin Costello, Jacob McNamara and Cumrun Vafa, 17006.09977
• Holography and Koszul duality: the example of the M2 brane, Kevin Costello, 1705.02500
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory, 1610.04144
• Twisted supergravity and its quantization, Kevin Costello and Si Li, 1606.00365
• Quantization of open-closed BCOV theory, I. Kevin Costello and Si Li. 1505.06703
• Integrable lattice models from four-dimensional field theories, Kevin Costello, 1308.0370
• Supersymmetric gauge theory and the Yangian, Kevin Costello, 1303.2632
• Factorization algebras in quantum field theories, volume 1, Cambridge University Press.

Seminars

• Plenary lecture at String Math 2020
• Western hemisphere colloquium on geometry and physics
• Harvard CMSA colloquium
• HEP theory seminar at IAS
• Between topology and quantum field theory, in honour of Dan Freed, UT Austin
• Invited lecture at a workshop on "Structures in enumerative geometry", MSRI, Berkeley.
• Chern-Simons workshop on Integrability across mathematics and physics
• Plenary talk at String-math 2017, Hamburg.
• Two lectures at Unversity of Chicago theoretical physics seminar
• Strings 2016, Beijing
• 6d little string theory, Peking University, Beijing
• Geometric unification from 6 dimensional physics, Banff
• The mathematics of quantum theory (in honour of Albert Schwarz), Davis California
• PIRSA:16060125, Learning Seminar on Maulik-Okounkov, 2016-06-23, Mathematical Physics
• PIRSA:16040069, Welcome and Opening Remarks, 2016-04-18, Deformation Quantization of Shifted Poisson Structures
• PIRSA:15100072, Basic aspects of 3d N=4 theories and symplectic duality, 2015-10-15, Mathematical Physics
• PIRSA:15090070, Condensed Matter and TFT Learning - An Overview, 2015-09-23, Mathematical Physics
• PIRSA:15040181, TBA, 2015-04-22, Superstring Perturbation Theory
• PIRSA:14100104, A Mathematician Looks at Supergravity and AdS/CFT, 2014-10-22, Superstring Perturbation Theory
• PIRSA:13030115, Supersymmetric gauge theory and the Yangian - continued, 2013-03-26, Colloquium
• PIRSA:13030114, Supersymmetric gauge theory and the Yangian, 2013-03-25, Colloquium