Dr Arick Shao
Reader in Mathematics
School of Mathematical Sciences
Queen Mary University of London
Queen Mary University of London
Research
Partial differential equations, Analysis, Differential geometry, Mathematical relativity, Unique continuation, Control theory
Interests
Partial differential equations (hyperbolic, dispersive, and parabolic equations)Mathematical analysis
Differential geometry
Mathematical relativity
Unique continuation and control theory of PDEs
Publications
Publications of specific relevance to the Centre for Geometry, Analysis and Gravitation2024
Shao A and Vergara B (2024). Approximate boundary controllability for parabolic equations with inverse square infinite potential wells. Nonlinear Analysis, Elsevier vol. 248 01-11-2024
Shao CT and Guisset S (2024). On counterexamples to unique continuation for critically singular wave equations. Journal of Differential Equations, Elsevier 08-03-2024
Shao A (2024). Control of Parabolic Equations with Inverse Square Infinite Potential Wells. Extended Abstracts 2021/2022 177-188. 01-01-2024
Shao A (2024). Bulk-Boundary Correspondences and Unique Continuation in Asymptotically Anti-de Sitter Spacetimes. 2021-2022 MATRIX Annals 231-273. 01-01-2024
Jena VK and Shao A (2024). Control of waves on Lorentzian manifolds with curvature bounds. ESAIM Control Optimisation and Calculus of Variations, EDP Sciences vol. 30 01-01-2024
2023
Holzegel G and Shao A (2023). The Bulk-Boundary Correspondence for the Einstein Equations in Asymptotically Anti-de Sitter Spacetimes. Archive for Rational Mechanics and Analysis, Springer Nature vol. 247 (3) 26-05-2023
2022
Dongbing L and Shao A (2022). Global stability of traveling waves for (1 + 1)-dimensional systems of quasilinear wave equations. Journal of Hyperbolic Differential Equations, World Scientific Publishing vol. 19 (04), 549-586. 01-12-2022
Shao CT and Chatzikaleas A (2022). A gauge-invariant unique continuation criterion for waves in asymptotically Anti-de Sitter spacetimes. Communications in Mathematical Physics, Springer 06-07-2022
2021
Enciso A, Shao A and Vergara B (2021). Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials. Journal of the European Mathematical Society, European Mathematical Society - EMS - Publishing House GmbH vol. 23 (10), 3459-3495. 08-06-2021
2020
McGill A and Shao A (2020). Null geodesics and improved unique continuation for waves in asymptotically Anti-de Sitter spacetimes. Classical and Quantum Gravity, IOP Publishing 02-12-2020
Shao A (2020). The near-boundary geometry of Einstein-vacuum asymptotically Anti-de Sitter spacetimes. Classical and Quantum Gravity, IOP Publishing 05-11-2020
2019
Shao CT (2019). On Carleman and observability estimates for wave equations on time-dependent domains. Proceedings of the London Mathematical Society, London Mathematical Society 10-05-2019
2017
SHAO CTA and Holzegel G (2017). Unique Continuation from Infinity in Asymptotic Anti-de Sitter Spacetimes II: Non-static Boundaries. Communications in Partial Differential Equations, Taylor & Francis 27-11-2017
Alexakis S and Shao A (2017). On the profile of energy concentration at blow-up points for subconformal focusing nonlinear waves. Transactions of the American Mathematical Society, 1-1. 13-02-2017
2016
Alexakis S and Shao A (2016). Bounds on the Bondi energy by a flux of curvature. Journal of the European Mathematical Society, European Mathematical Society - EMS - Publishing House vol. 18 (9), 2045-2106. 25-07-2016
Holzegel G and Shao A (2016). Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes. Communications in Mathematical Physics 24-02-2016
Alexakis S, Schlue V and Shao A (2016). Unique continuation from infinity for linear waves. Advances in Mathematics, Elsevier vol. 286, 481-544. 01-01-2016
2015
Alexakis S and Shao A (2015). Global uniqueness theorems for linear and nonlinear waves. Journal of Functional Analysis, Elsevier vol. 269 (11), 3458-3499. 01-12-2015
2014
Shao A (2014). New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problems. Journal of Hyperbolic Differential Equations, World Scientific Publishing vol. 11 (04), 821-908. 01-12-2014
Alexakis S and Shao A (2014). On the geometry of null cones to infinity under curvature flux bounds. Classical and Quantum Gravity vol. 31 (19), 195012-195012. 22-09-2014
2013
Egli D, Fröhlich J, Gang Z, Shao A and Sigal IM (2013). Hamiltonian Dynamics of a Particle Interacting with a Wave Field. Communications in Partial Differential Equations vol. 38 (12), 2155-2198. 02-12-2013
2011
Shao A (2011). A Generalized Representation Formula for Systems of Tensor Wave Equations. Communications in Mathematical Physics vol. 306 (1), 51-82. 28-05-2011
Shao A (2011). On Breakdown Criteria for Nonvacuum Einstein Equations. Annales Henri Poincaré vol. 12 (2), 205-277. 08-02-2011
Grants
Grants of specific relevance to the Centre for Geometry, Analysis and GravitationAstronomy Research at Queen Mary 2023 - 2026Chris Clarkson, Richard Nelson, Timothy Clifton, William Sutherland, Edward Gillen, Karim Malik, Thomas Haworth, Sijme-Jan Paardekooper, Theresa Baker, David Mulryne, Philip Bull, Juan A. Valiente Kroon, Charalampos Markakis, Mohammad Mahdi Godazgar, Katy Clough, Pau Figueras and Arick Shao
£1,625,769 Science & Technology Research Council (STFC) (01-04-2023 - 30-09-2026)
Rigidity Problems in Holography and RelativityArick Shao
£77,733 EPSRC Engineering and Physical Sciences Research Council (01-01-2024 - 31-12-2024)
Unique continuation for geometric wave equationsArick Shao
£100,892 EPSRC Engineering and Physical Sciences Research Council (01-02-2018 - 31-01-2020)