Dr Arick ShaoReader in MathematicsEmail: a.shao@qmul.ac.ukTelephone: +44 (0)20 7882 8511Room Number: Mathematical Sciences Building, Room: MB-513Website: http://www.maths.qmul.ac.uk/~shao/Office Hours: Friday 11:30-12:30 Other times by e-mail appointments.ProfileResearchPublicationsProfileArick 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.ResearchResearch Interests:Partial differential equations (wave equations, hyperbolic PDE, dispersive PDE, geometric PDE), analysis, mathematical relativity, differential geometryPublications Shao A, Vergara B (2024). Approximate boundary controllability for parabolic equations with inverse square infinite potential wells Nonlinear Analysis nameOfConference. 10.1016/j.na.2024.113624 https://qmro.qmul.ac.uk/xmlui/handle/123456789/98363 Jena VK, Shao A (2024). Control of waves on Lorentzian manifolds with curvature bounds ESAIM Control Optimisation and Calculus of Variations nameOfConference. 10.1051/cocv/2024056 https://qmro.qmul.ac.uk/xmlui/handle/123456789/98583 Shao A (2024). Bulk-Boundary Correspondences and Unique Continuation in Asymptotically Anti-de Sitter Spacetimes journal nameOfConference. 10.1007/978-3-031-47417-0_13 qmroHref Shao CT, Guisset S (2024). On counterexamples to unique continuation for critically singular wave equations Journal of Differential Equations nameOfConference. 10.1016/j.jde.2024.02.031 https://qmro.qmul.ac.uk/xmlui/handle/123456789/94718 Shao A (2024). Control of Parabolic Equations with Inverse Square Infinite Potential Wells journal nameOfConference. 10.1007/978-3-031-48579-4_18 qmroHref 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 nameOfConference. 10.1007/s00205-023-01890-9 https://qmro.qmul.ac.uk/xmlui/handle/123456789/86879 Dongbing L, Shao A (2022). Global stability of traveling waves for (1 + 1)-dimensional systems of quasilinear wave equations Journal of Hyperbolic Differential Equations nameOfConference. 10.1142/s0219891622500163 https://qmro.qmul.ac.uk/xmlui/handle/123456789/78982 Shao CT, Chatzikaleas A (2022). A gauge-invariant unique continuation criterion for waves in asymptotically Anti-de Sitter spacetimes Communications in Mathematical Physics nameOfConference. 10.1007/s00220-022-04434-6 https://qmro.qmul.ac.uk/xmlui/handle/123456789/78983 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 nameOfConference. 10.4171/jems/1105 https://qmro.qmul.ac.uk/xmlui/handle/123456789/62369 McGill A, Shao A (publicationYear). Null geodesics and improved unique continuation for waves in asymptotically Anti-de Sitter spacetimes Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/abcfd1 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/69392 Shao A (publicationYear). The near-boundary geometry of Einstein-vacuum asymptotically Anti-de Sitter spacetimes Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/abc81a https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/68500 Shao CT (2019). On Carleman and observability estimates for wave equations on time-dependent domains Proceedings of the London Mathematical Society nameOfConference. 10.1112/plms.12253 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/57663 SHAO CTA, Holzegel G (publicationYear). Unique Continuation from Infinity in Asymptotic Anti-de Sitter Spacetimes II: Non-static Boundaries Communications in Partial Differential Equations nameOfConference. 10.1080/03605302.2017.1390677 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/25967 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 nameOfConference. 10.1090/tran/6820 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16077 Alexakis S, Shao A (2016). Bounds on the Bondi energy by a flux of curvature Journal of the European Mathematical Society nameOfConference. 10.4171/jems/638 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/17710 Holzegel G, Shao A (publicationYear). Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes Communications in Mathematical Physics nameOfConference. 10.1007/s00220-016-2576-0 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16076 Alexakis S, Schlue V, Shao A (2016). Unique continuation from infinity for linear waves Advances in Mathematics nameOfConference. 10.1016/j.aim.2015.08.028 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16074 Alexakis S, Shao A (2015). Global uniqueness theorems for linear and nonlinear waves Journal of Functional Analysis nameOfConference. 10.1016/j.jfa.2015.08.012 https://qmro.qmul.ac.uk/xmlui/handle/123456789/16075 Shao A (2014). New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problems Journal of Hyperbolic Differential Equations nameOfConference. 10.1142/s0219891614500258 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16071 Alexakis S, Shao A (2014). On the geometry of null cones to infinity under curvature flux bounds Classical and Quantum Gravity nameOfConference. 10.1088/0264-9381/31/19/195012 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16073 Egli D, Fröhlich J, Gang Z et al. (2013). Hamiltonian Dynamics of a Particle Interacting with a Wave Field Communications in Partial Differential Equations nameOfConference. 10.1080/03605302.2013.816857 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16072 Shao A (2011). A Generalized Representation Formula for Systems of Tensor Wave Equations Communications in Mathematical Physics nameOfConference. 10.1007/s00220-011-1273-2 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16070 Shao A (2011). On Breakdown Criteria for Nonvacuum Einstein Equations Annales Henri Poincaré nameOfConference. 10.1007/s00023-011-0082-7 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/16069