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Jason D. Lotay


Jason D. Lotay
Professor of Pure Mathematics
University of Oxford
Fellow at Balliol College


PUBLICATIONS

PREPRINTS

CONFERENCE PROCEEDINGS

PUBLIC ENGAGEMENT

BOOKS


Publications

  1. with G. Oliveira, Examples of Deformed G2-instantons/Donaldson-Thomas Connections, to appear in Annales de l'Institut Fourier. [arXiv:2007.11304]

  2. with B. Lambert and F. Schulze, Ancient Solutions in Lagrangian Mean Curvature Flow, to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. [arXiv:1901.05383]

  3. with S. Karigiannis, Bryant-Salamon G2 manifolds and Coassociative Fibrations, Journal of Geometry and Physics 162 (2021), 104074. [arXiv:2002.06444]

  4. with B. Lambert, Spacelike Mean Curvature Flow, Journal of Geometric Analysis 31 (2021), 1291-1359. [arXiv:1808.01994]

  5. with C.G. Evans and F. Schulze, Remarks on the Self-shrinking Clifford Torus, Journal für die Reine und Angewandte Mathematik 2020 (2020), 139-170. [arXiv:1802.01423]

  6. with S. Karigiannis, Deformation Theory of G2 Conifolds, Communications in Analysis and Geometry 28 (2020), 1057-1210. [arXiv:1212.6457]

  7. with T. Pacini, From Lagrangian to Totally Real Geometry: Coupled Flows and Calibrations, Communications in Analysis and Geometry 28 (2020), 607-675. [arXiv:1404.4227]

  8. with F. Schulze, Consequences of Strong Stability of Minimal Submanifolds, International Mathematics Research Notices 2020 (2020), 2352-2360. [arXiv:1802.03941]

  9. with Y. Wei, Laplacian Flow for Closed G2 Structures: Real Analyticity, Communications in Analysis and Geometry 27 (2019), 73-109. [arXiv:1601.04258]

  10. with Y. Wei, Stability of Torsion-free G2 Structures along the Laplacian Flow, Journal of Differential Geometry 111 (2019), 495-526. [arXiv:1504.07771]

  11. with T. Pacini, Complexified Diffeomorphism Groups, Totally Real Submanifolds and Kähler-Einstein Geometry, Transactions of the American Mathematical Society 371 (2019), 2665-2701. [arXiv:1506.04630]

  12. with T. Pacini, From Minimal Lagrangian to J-minimal Submanifolds: Persistence and Uniqueness, Bollettino dell'Unione Matematica Italiana 12 (2019), 63-82: a special issue in memory of Paolo de Bartolomeis. [arXiv:1704.08226]

  13. with G. Oliveira, SU(2)2-invariant G2-instantons, Mathematische Annalen 371 (2018), 961-1011. [arXiv:1608.07789]

  14. with J. Fine and M. Singer, The Space of Hyperkähler Metrics on a 4-Manifold with Boundary, Forum of Mathematics, Sigma 5 (2017). [arXiv:1603.08170]

  15. with Y. Wei, Laplacian Flow for Closed G2 Structures: Shi-type Estimates, Uniqueness and Compactness, Geometric and Functional Analysis 27 (2017), 165-233. [arXiv:1504.07367]

  16. Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications, Transactions of the American Mathematical Society 366 (2014), 6051-6092. [arXiv:1209.5116]

  17. with A. Neves, Uniqueness of Lagrangian Self-expanders, Geometry and Topology 17 (2013), 2689-2729. [arXiv:1208.2729]

  18. Associative Submanifolds of the 7-Sphere, Proceedings of the London Mathematical Society 105 (2012), 1183-1214. [arXiv:1006.0361]

  19. Stability of Coassociative Conical Singularities, Communications in Analysis and Geometry 20 (2012), 803-867. [arXiv:0910.5092]

  20. Ruled Lagrangian Submanifolds of the 6-Sphere, Transactions of the American Mathematical Society 363 (2011), 2305-2339. [arXiv:0807.2084]

  21. Asymptotically Conical Associative 3-folds, The Quarterly Journal of Mathematics 62 (2011), 131-156. [arXiv:0802.3536]

  22. Deformation Theory of Asymptotically Conical Coassociative 4-folds, Proceedings of the London Mathematical Society 99 (2009), 386-424. [arXiv:math/0411116]

  23. with A. Kovalev, Deformations of Compact Coassociative 4-folds with Boundary, Journal of Geometry and Physics 59 (2009), 63-73. [arXiv:0712.4325]

  24. Desingularization of Coassociative 4-folds with Conical Singularities, Geometric and Functional Analysis 18 (2008), 2055-2100. [arXiv:math/0611183]

  25. Coassociative 4-folds with Conical Singularities, Communications in Analysis and Geometry 15 (2007), 891-946. [arXiv:math/0601762]

  26. Calibrated Submanifolds of R7 and R8 with Symmetries, The Quarterly Journal of Mathematics 58 (2007), 53-70. [arXiv:math/0601764]

  27. 2-Ruled Calibrated 4-folds in R7 and R8, Journal of the London Mathematical Society 74 (2006), 219-243. [arXiv:math/0401125]

  28. Constructing Associative 3-folds by Evolution Equations, Communications in Analysis and Geometry 13 (2005), 999-1037. [arXiv:math/0401123]


Preprints

  1. with H. Sá Earp, The Heterotic G2 System on Contact Calabi-Yau 7-manifolds, 2021. [arXiv:2101.06767]

  2. with G. Oliveira, Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz, 2020. [arXiv:2002.10391]


Conference proceedings

  1. Examples of Equivariant Lagrangian Mean Curvature Flow, to appear in Proceedings of the 2019 ISAAC Congress (Aveiro, Portugal), 2020. [arXiv:2008.08067]

  2. Ancient Solutions in Lagrangian Mean Curvature Flow, in Oberwolfach Report 30/2019, 2019. [preliminary version]

  3. with G. Oliveira, G2-instantons on noncompact G2-manifolds: results and open problems, in Lectures and Surveys on G2 manifolds and related topics, Fields Institute Communications. [arXiv:1812.11867] [book]

  4. Geometric Flows of G2 Structures, in Lectures and Surveys on G2 manifolds and related topics, Fields Institute Communications. [arXiv:1810.13417] [book]

  5. Calibrated Submanifolds, in Lectures and Surveys on G2 manifolds and related topics, Fields Institute Communications. [arXiv:1810.08709] [book]

  6. with T. Madsen, Instantons and Special Geometry, in Special Metrics and Group Actions in Geometry, 2017. [book]

  7. Deformations of G2 Manifolds, in Oberwolfach Report 8/2015, 2015. [final version]

  8. Uniqueness of Lagrangian Self-expanders, in Proceedings of PADGE2012, 2013. [book]


Public engagement

  1. Por qué estudio la séptima dimensión, Café y Teoremas, El País, November 2018. [article]

  2. The Geometry of Our World, feature article, Physics World, April 2017. [article]

  3. Adventures in the 7th Dimension, expository article, UCL De Morgan Newsletter, April 2017.

  4. Seeing in 4D, expository article, UCL De Morgan Newsletter, December 2015.

  5. Take Your Brain to Another Dimension, expository article, UCL De Morgan Newsletter, December 2015.

  6. Art and Maths Workshops, expository article, UCL De Morgan Newsletter, December 2014.



Books

  1. Editor: with S. Karigannis and N. C. Leung, Lectures and Surveys on G2-Manifolds and Related Topics, Fields Institute Communications, Springer, 2020. [Springer website]