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. 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
- Simons collaboration in celestial holography, Simons Foundation, 2023-2027
- John L. Synge award, Royal Society of Canada, 2022
- Discovery Grant, Natural Sciences and Engineering Research Council of Canada (NSERC), 2021
- Leonard Eisenbud Prize for Mathematics and Physics, American Mathematical Society, 2020
- Honorary Member, Royal Irish Academy, 2020
- Fellow, Royal Society, 2018
- Berwick Prize, London Mathematical Society, 2017
Recent Publications
- Costello, K., Paquette, N. M., & Sharma, A. (n.d.). Burns space and holography. Journal of High Energy Physics, 2023(10). doi:10.1007/jhep10(2023)174
- Costello, K., Paquette, N. M., & Sharma, A. (2023). Burns space and holography. arxiv:2306.00940v2
- Costello, K., Dimofte, T., & Gaiotto, D. (2023). Boundary Chiral Algebras and Holomorphic Twists. Communications in Mathematical Physics, 399(2), 1203-1290. doi:10.1007/s00220-022-04599-0
- Costello, K., Paquette, N. M., & Sharma, A. (n.d.). Top-Down Holography in an Asymptotically Flat Spacetime. Physical Review Letters, 130(6). doi:10.1103/physrevlett.130.061602
- Costello, K. J. (2023). Bootstrapping two-loop QCD amplitudes. arxiv:2302.00770v2
- Costello, K., & Paquette, N. M. (n.d.). Associativity of One-Loop Corrections to the Celestial Operator Product Expansion. Physical Review Letters, 129(23). doi:10.1103/physrevlett.129.231604
- Costello, K., & Paquette, N. M. (n.d.). Celestial holography meets twisted holography: 4d amplitudes from chiral correlators. Journal of High Energy Physics, 2022(10). doi:10.1007/jhep10(2022)193
- Costello, K., & Paquette, N. M. (2022). On the associativity of one-loop corrections to the celestial OPE. arxiv:2204.05301v1
- Costello, K., & Zwiebach, B. (2022). Hyperbolic string vertices. Journal of High Energy Physics, 2022(2). doi:10.1007/jhep02(2022)002
- Costello, K. J. (2021). Quantizing local holomorphic field theories on twistor space. arxiv:2111.08879v1
- Costello, K., & Williams, B. R. (2021). Twisted heterotic/type I duality. arxiv:2110.14616v1
- Costello, K., & Paquette, N. M. (2021). Twisted Supergravity and Koszul Duality: A Case Study in AdS$$_3$$. Communications in Mathematical Physics, 384(1), 279-339. doi:10.1007/s00220-021-04065-3
- Costello, K., Gaiotto, D., & Yagi, J. (2021). Q-operators are 't Hooft lines. arxiv:2103.01835v1
- Costello, K., & Stefanski, B. (n.d.). Chern-Simons Origin of Superstring Integrability. Physical Review Letters, 125(12). doi:10.1103/physrevlett.125.121602
- Caldararu, A., Costello, K., & Tu, J. (2020). Categorical Enumerative Invariants, I: String vertices. arxiv:2009.06673v1
- Costello, K., Dimofte, T., & Gaiotto, D. (2020). Boundary Chiral Algebras and Holomorphic Twists. arxiv:2005.00083v1
- Costello, K., & Yagi, J. (2020). Unification of integrability in supersymmetric gauge theories. Advances in Theoretical and Mathematical Physics, 24(8), 1931-2041. doi:10.4310/atmp.2020.v24.n8.a1
- Costello, K., & Li, S. (2020). Anomaly cancellation in the topological string. Advances in Theoretical and Mathematical Physics, 24(7), 1723-1771. doi:10.4310/atmp.2020.v24.n7.a2
Seminars
- Twisted Holography Mini-Course - Lecture 20231116, Twisted Holography Mini-Course, 2023/11/16, PIRSA:23110040
- Twisted Holography Mini-Course - Lecture 20231109, Twisted Holography Mini-Course, 2023/11/09, PIRSA:23110039
- Twisted Holography Mini-Course - Lecture 20231102, Twisted Holography Mini-Course, 2023/11/02, PIRSA:23110038
- Twistors and factorization algebras, Homotopy and operator algebras in QFT, Humboldt-Universität zu Berlin, Berlin, Germany, 2023/06/05
- Mathematical Physics Lecture (230505), Mathematical Physics - Elective (2022/2023), 2023/05/05, PIRSA:23050012
- Mathematical Physics Lecture (230503), Mathematical Physics - Elective (2022/2023), 2023/05/03, PIRSA:23050011
- Mathematical Physics Lecture (230501), Mathematical Physics - Elective (2022/2023), 2023/05/01, PIRSA:23050010
- Burns space and holography, New England string meeting, Brown University, Physics; Brown University, Providence, United States, 2023/04/28
- Bootstrapping two-loop QCD amplitudes, Harvard HET seminar, Harvard University, Physics, Cambridge, United States, 2023/04/27
- Mathematical Physics Lecture (230421), Mathematical Physics - Elective (2022/2023), 2023/04/21, PIRSA:23040050
- Mathematical Physics Lecture (230419), Mathematical Physics - Elective (2022/2023), 2023/04/19, PIRSA:23040049
- Mathematical Physics Lecture (230404), Mathematical Physics - Elective (2022/2023), 2023/04/18, PIRSA:23040077
- Mathematical Physics Lecture (230417), Mathematical Physics - Elective (2022/2023), 2023/04/17, PIRSA:23040048
- Mathematical Physics Lecture (230414), Mathematical Physics - Elective (2022/2023), 2023/04/14, PIRSA:23040047
- Mathematical Physics Lecture (230412), Mathematical Physics - Elective (2022/2023), 2023/04/12, PIRSA:23040046
- Mathematical Physics Lecture (230404), Mathematical Physics - Elective (2022/2023), 2023/04/11, PIRSA:23040076
- Mathematical Physics Lecture (230405), Mathematical Physics - Elective (2022/2023), 2023/04/05, PIRSA:23040043
- Mathematical Physics Lecture (230404), Mathematical Physics - Elective (2022/2023), 2023/04/04, PIRSA:23040075
- Mathematical Physics Lecture (230403), Mathematical Physics - Elective (2022/2023), 2023/04/03, PIRSA:23040042
- Mathematical Physics Lecture - 230207, Mathematical Physics (2022/2023), 2023/02/07, PIRSA:23020005
- Mathematical Physics Lecture - 230202, Mathematical Physics (2022/2023), 2023/02/02, PIRSA:23020004
- Mathematical Physics Lecture - 230131, Mathematical Physics (2022/2023), 2023/01/31, PIRSA:23010018
- Mathematical Physics Lecture - 230127, Mathematical Physics (2022/2023), 2023/01/27, PIRSA:23010021
- Mathematical Physics Lecture - 230126, Mathematical Physics (2022/2023), 2023/01/26, PIRSA:23010017
- Mathematical Physics Lecture - 230124, Mathematical Physics (2022/2023), 2023/01/24, PIRSA:23010016
- Mathematical Physics Lecture - 230119, Mathematical Physics (2022/2023), 2023/01/19, PIRSA:23010015
- Mathematical Physics Lecture - 230118, Mathematical Physics (2022/2023), 2023/01/18, PIRSA:23010022
- Mathematical Physics Lecture - 230117, Mathematical Physics (2022/2023), 2023/01/17, PIRSA:23010014
- Top-down asymptotically flat holography, Tata Institute of Fundamental Research, Mumbai, India, 2022/10/28
- Welcome and Opening Remarks, QFT for Mathematicians 2022, 2022/06/20, PIRSA:22060062
- 3d Theories and Twists I, QFT for Mathematicians 2022, 2022/06/20, PIRSA:22060063
- Vertex algebras and self-dual Yang-Mills theory, Global Categorical Symmetries, 2022/06/06, PIRSA:22060009
- Geometry and topology for physicists 2021/2022 - Lecture 14, Geometry and Topology for Physicists 2021/2022, 2022/03/31, PIRSA:22030072
- Geometry and topology for physicists 2021/2022 - Lecture 13, Geometry and Topology for Physicists 2021/2022, 2022/03/29, PIRSA:22030071
- Geometry and topology for physicists 2021/2022 - Lecture 12, Geometry and Topology for Physicists 2021/2022, 2022/03/25, PIRSA:22030070
- Geometry and topology for physicists 2021/2022 - Lecture 10, Geometry and Topology for Physicists 2021/2022, 2022/03/22, PIRSA:22030068
- Geometry and topology for physicists 2021/2022 - Lecture 9, Geometry and Topology for Physicists 2021/2022, 2022/03/18, PIRSA:22030067
- Geometry and topology for physicists 2021/2022 - Lecture 8, Geometry and Topology for Physicists 2021/2022, 2022/03/17, PIRSA:22030066
- Geometry and topology for physicists 2021/2022 - Lecture 7, Geometry and Topology for Physicists 2021/2022, 2022/03/15, PIRSA:22030065
- Geometry and topology for physicists 2021/2022 - Lecture 6, Geometry and Topology for Physicists 2021/2022, 2022/03/11, PIRSA:22030064
- Geometry and topology for physicists 2021/2022 - Lecture 5, Geometry and Topology for Physicists 2021/2022, 2022/03/10, PIRSA:22030063
- Geometry and topology for physicists 2021/2022 - Lecture 4, Geometry and Topology for Physicists 2021/2022, 2022/03/08, PIRSA:22030062
- Geometry and topology for physicists 2021/2022 - Lecture 3, Geometry and Topology for Physicists 2021/2022, 2022/03/04, PIRSA:22030061
- Geometry and topology for physicists 2021/2022 - Lecture 2, Geometry and Topology for Physicists 2021/2022, 2022/03/03, PIRSA:22030060
- Geometry and topology for physicists 2021/2022 - Lecture 1, Geometry and Topology for Physicists 2021/2022, 2022/03/01, PIRSA:22030059
- Seminar, Spring School on Superstring Theory and Related Topics, Trieste, Italy, 2022/01/01
- HEP Theory Seminar, Institute for Advanced Studies, 2022/01/01
- Seminar, International Centre for Theoretical Sciences, Bengaluru, India, 2022/01/01
- On the crossroads of algebra geometry and physics, Conference in honour of Sasha Goncharov, 2022/01/01
- Mathematical Physics Seminar, One World IAMP, 2022/01/01
- Invited Lecture, Strings 2021, ICTP-SAIFR, São Paulo, Brazil, 2021/06/30
- Seminar, Ludwig-Maximilians-Universität München, Munich, Germany, 2021/01/01
- Séminaire Physique Mathématique, Montreal, Quebec, 2021/01/01
- String Theory Seminar, European Organization for Nuclear Research (CERN), Geneva, Switzerland, 2021/01/01