Dr Arick Shao
Reader in Mathematics
Email: a.shao@qmul.ac.uk
Telephone: +44 (0)20 7882 8511
Room Number: Mathematical Sciences Building, Room: MB-513
Website: http://www.maths.qmul.ac.uk/~shao/
Office Hours: Friday 11:30-12:30
Other times by e-mail appointments.
Profile
Arick Shao is a Reader in Mathematics at the School of Mathematical Sciences, and he is a member of the Geometry and Analysis research group. His primary research interests lie in partial differential equations, mathematical analysis, differential geometry, and mathematical relativity.
Prior to joining Queen Mary University of London, Dr. Shao was a Research Associate at Imperial College London and a Postdoctoral Fellow at the University of Toronto. He holds a PhD in Mathematics from Princeton University.
Research
Research Interests:
Partial differential equations (wave equations, hyperbolic PDE, dispersive PDE, geometric PDE), analysis, mathematical relativity, differential geometry
Publications
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Shao A, Vergara B (2024). Approximate boundary controllability for parabolic equations with inverse square infinite potential wells Nonlinear Analysis .
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Jena VK, Shao A (2024). Control of waves on Lorentzian manifolds with curvature bounds ESAIM Control Optimisation and Calculus of Variations .
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Shao A (2024). Bulk-Boundary Correspondences and Unique Continuation in Asymptotically Anti-de Sitter Spacetimes .
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Shao CT, Guisset S (2024). On counterexamples to unique continuation for critically singular wave equations Journal of Differential Equations .
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Shao A (2024). Control of Parabolic Equations with Inverse Square Infinite Potential Wells .
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Holzegel G, Shao A (2023). The Bulk-Boundary Correspondence for the Einstein Equations in Asymptotically Anti-de Sitter Spacetimes Archive for Rational Mechanics and Analysis .
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Dongbing L, Shao A (2022). Global stability of traveling waves for (1 + 1)-dimensional systems of quasilinear wave equations Journal of Hyperbolic Differential Equations .
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Shao CT, Chatzikaleas A (2022). A gauge-invariant unique continuation criterion for waves in asymptotically Anti-de Sitter spacetimes Communications in Mathematical Physics .
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Enciso A, Shao A, Vergara B (2021). Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials Journal of the European Mathematical Society .
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McGill A, Shao A . Null geodesics and improved unique continuation for waves in asymptotically Anti-de Sitter spacetimes Classical and Quantum Gravity .
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Shao A . The near-boundary geometry of Einstein-vacuum asymptotically Anti-de Sitter spacetimes Classical and Quantum Gravity .
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Shao CT (2019). On Carleman and observability estimates for wave equations on time-dependent domains Proceedings of the London Mathematical Society .
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SHAO CTA, Holzegel G . Unique Continuation from Infinity in Asymptotic Anti-de Sitter Spacetimes II: Non-static Boundaries Communications in Partial Differential Equations .
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Alexakis S, Shao A (2017). On the profile of energy concentration at blow-up points for subconformal focusing nonlinear waves Transactions of the American Mathematical Society .
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Alexakis S, Shao A (2016). Bounds on the Bondi energy by a flux of curvature Journal of the European Mathematical Society .
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Holzegel G, Shao A . Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes Communications in Mathematical Physics .
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Alexakis S, Schlue V, Shao A (2016). Unique continuation from infinity for linear waves Advances in Mathematics .
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Alexakis S, Shao A (2015). Global uniqueness theorems for linear and nonlinear waves Journal of Functional Analysis .
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Shao A (2014). New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problems Journal of Hyperbolic Differential Equations .
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Alexakis S, Shao A (2014). On the geometry of null cones to infinity under curvature flux bounds Classical and Quantum Gravity .
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Egli D, Fröhlich J, Gang Z et al. (2013). Hamiltonian Dynamics of a Particle Interacting with a Wave Field Communications in Partial Differential Equations .
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Shao A (2011). A Generalized Representation Formula for Systems of Tensor Wave Equations Communications in Mathematical Physics .
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Shao A (2011). On Breakdown Criteria for Nonvacuum Einstein Equations Annales Henri Poincaré .