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
On counterexamples to unique continuation for critically singular wave equationsShao CT Guisset S
Journal of Differential Equations, Elsevier
08-03-2024
Control of Parabolic Equations with Inverse Square Infinite Potential WellsShao A
In Extended Abstracts 2021/2022, Springer Nature 177-188.
01-01-2024
Bulk-Boundary Correspondences and Unique Continuation in Asymptotically Anti-de Sitter SpacetimesShao A
In 2021-2022 Matrix Annals, Springer Nature 231-273.
01-01-2024
2023
The Bulk-Boundary Correspondence for the Einstein Equations in Asymptotically Anti-de Sitter SpacetimesShao CT Holzegel G
Archive For Rational Mechanics and Analysis, Springer
26-05-2023
2022
A gauge-invariant unique continuation criterion for waves in asymptotically Anti-de Sitter spacetimesShao CT Chatzikaleas A
Communications in Mathematical Physics, Springer
06-07-2022
2021
Control of waves on Lorentzian manifolds with curvature boundsJena VK Shao A
In Arxiv
17-12-2021
Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentialsEnciso A Shao A Vergara B
Journal of The European Mathematical Society, European Mathematical Society - Ems - Publishing House Gmbh vol. 23 (10), 3459-3495.
08-06-2021
2020
Null geodesics and improved unique continuation for waves in asymptotically Anti-de Sitter spacetimesMcGill A Shao A
Classical and Quantum Gravity, Iop Publishing
02-12-2020
The near-boundary geometry of Einstein-vacuum asymptotically Anti-de Sitter spacetimesShao A
Classical and Quantum Gravity, Iop Publishing
05-11-2020
2019
On Carleman and observability estimates for wave equations on time-dependent domainsShao CT
Proceedings of The London Mathematical Society, London Mathematical Society
10-05-2019
2017
Unique Continuation from Infinity in Asymptotic Anti-de Sitter Spacetimes II: Non-static BoundariesSHAO CTA Holzegel G
Communications in Partial Differential Equations, Taylor & Francis
27-11-2017
On the profile of energy concentration at blow-up points for subconformal focusing nonlinear wavesAlexakis S Shao A
Transactions of The American Mathematical Society, 1-1.
13-02-2017
2016
Bounds on the Bondi energy by a flux of curvatureAlexakis S Shao A
Journal of The European Mathematical Society, European Mathematical Society - Ems - Publishing House vol. 18 (9), 2045-2106.
25-07-2016
Unique Continuation from Infinity in Asymptotically Anti-de Sitter SpacetimesHolzegel G Shao A
Communications in Mathematical Physics
24-02-2016
2014
On the geometry of null cones to infinity under curvature flux boundsAlexakis S Shao A
Classical and Quantum Gravity vol. 31 (19), 195012-195012.
22-09-2014
2013
Hamiltonian Dynamics of a Particle Interacting with a Wave FieldEgli D Fröhlich J Gang Z Shao A Sigal IM
Communications in Partial Differential Equations vol. 38 (12), 2155-2198.
02-12-2013
2011
A Generalized Representation Formula for Systems of Tensor Wave EquationsShao A
Communications in Mathematical Physics vol. 306 (1), 51-82.
28-05-2011
On Breakdown Criteria for Nonvacuum Einstein EquationsShao A
Annales Henri Poincaré vol. 12 (2), 205-277.
08-02-2011
Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimatesShao CT Enciso A Vergara B
Analysis & Pde, Mathematical Sciences Publishers (Msp)
New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problemsShao A
Journal of Hyperbolic Differential Equations vol. 11 (04), 821-908.
Unique continuation from infinity for linear wavesAlexakis S Schlue V Shao A
Advances in Mathematics vol. 286, 481-544.
Global uniqueness theorems for linear and nonlinear wavesAlexakis S Shao A
Journal of Functional Analysis vol. 269 (11), 3458-3499.
Global stability of traveling waves for (1+1)-dimensional systems of quasilinear wave equationsShao CT Zha D
Journal of Hyperbolic Differential Equations, World Scientific Publishing
The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimesShao CT Holzegel G
Archive For Rational Mechanics and Analysis, Springer
Approximate boundary controllability for parabolic equations with inverse square infinite potential wellsShao CT Vergara B
Nonlinear Analysis, Elsevier
Control of waves on Lorentzian manifolds with curvature boundsShao CT Jena V
Esaim: Control, Optimisation and Calculus of Variations, Edp Sciences
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 - 31-03-2027
Rigidity Problems in Holography and RelativityArick Shao
£77,733 EPSRC Engineering and Physical Sciences Research Council
Grant Summary
01-01-2024 - 31-12-2024
Unique continuation for geometric wave equationsArick Shao
£100,892 EPSRC Engineering and Physical Sciences Research Council
Grant Summary
01-02-2018 - 31-01-2020
Research Group
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