# Kevin Costello

Krembil William Rowan Hamilton Chair in Theoretical Physics

Perimeter Institute for Theoretical Physics

Areas of research:

### 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. Recently I have become interested in applying these methods to the study of four-dimensional models which are not too far from the models describing interactions of fundamental particles.

### 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

- Kevin Costello and Natalie Paquette, "Celestial holography meets twisted holography: 4d amplitudes from chiral correlators", accepted for publication in JHEP. https://arxiv.org/abs/2201.02595
- Quantizing local holomorphic field theories on twistor space, Kevin Costello https://arxiv.org/abs/2111.08879
- Twisted heterotic-type I duality, Kevin Costello and Brian Williams, https://arxiv.org/abs/2110.14616
- Q-operators are 't Hooft lines, 2103.01835
- Boundary Chiral Algebras and Holomorphic Twists, Kevin Costello, Tudor Dimofte, Davide Gaiotto 2005.00083
- The Chern-Simons Origin of Superstring Integrability, Kevin Costello, Bogdan StefaÅski jr , 2005.03064
- 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 theory, volume 2, Cambridge University Press. In press, see https://www.cambridge.org/core/books/factorization-algebras-in-quantum-field-theory/3B0E2ADE1EB6E0B06C91EA6E888B0C20
- Factorization algebras in quantum field theory, volume 1, Cambridge University Press.

### Seminars

- "On the crossroads of algebra geometry and physics", conference in honour of Sasha Goncharov
- Spring school on superstring theory and related topics, Trieste.
- One world IAMP mathematical physics seminar
- Seminar at ICTS, Banglaore
- HEP theory seminar at the Institute for Advanced Studies
- LMU Munich seminar
- Séminaire Physique Mathématique, Montreal
- Strings 2021, invited lecture
- Cern string theory seminar
- London Triangle Seminar
- Hamburg mathemaitcal physics colloquium
- York mathematical physics seminar
- Amsterdam string theory seminar
- Stanford string theory seminar,
- 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