Dr Arick Shao

Arick Shao

Reader in Mathematics

School of Mathematical Sciences
Queen Mary University of London
ResearcherID ORCID Google Scholar

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

Relevant PublicationPublications of specific relevance to the Centre for Geometry, Analysis and Gravitation

2024

Relevant PublicationShao CT and Guisset S (2024). On counterexamples to unique continuation for critically singular wave equations. Journal of Differential Equations, Elsevier 
08-03-2024

2023

Relevant PublicationHolzegel 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

Relevant PublicationDongbing 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
Relevant PublicationShao 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

Relevant PublicationEnciso 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

Relevant PublicationMcGill 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
Relevant PublicationShao A (2020). The near-boundary geometry of Einstein-vacuum asymptotically Anti-de Sitter spacetimes. Classical and Quantum Gravity, IOP Publishing 
05-11-2020

2019

Relevant PublicationShao 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

Relevant PublicationSHAO 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
Relevant PublicationAlexakis 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

Relevant PublicationAlexakis 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
Relevant PublicationHolzegel G and Shao A (2016). Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes. Communications in Mathematical Physics 
24-02-2016
Relevant PublicationAlexakis 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

Relevant PublicationAlexakis 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

Relevant PublicationShao 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
Relevant PublicationAlexakis 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

Relevant PublicationEgli 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

Relevant PublicationShao A (2011). A Generalized Representation Formula for Systems of Tensor Wave Equations. Communications in Mathematical Physics vol. 306 (1), 51-82.  
28-05-2011
Relevant PublicationShao A (2011). On Breakdown Criteria for Nonvacuum Einstein Equations. Annales Henri Poincaré vol. 12 (2), 205-277.  
08-02-2011

Grants

solid heart iconGrants of specific relevance to the Centre for Geometry, Analysis and Gravitation
solid heart iconAstronomy Research at Queen Mary 2023 - 2026
Christopher Clarkson, Richard Nelson, Timothy Clifton, William Sutherland, Edward Gillen, Karim Malik, Thomas James Haworth, Sijme-Jan Paardekooper, Theresa Baker, David Mulryne, Philip Bull, Juan Antonio Valiente Kroon, Charalampos Markakis, Mohammad Mahdi Godazgar, Katherine Clough, Pau Figueras and Chung Tse Shao
£1,625,769 Science & Technology Research Council (STFC) (01-04-2023 - 30-09-2026)
solid heart iconRigidity Problems in Holography and Relativity
Chung Tse Shao
£77,733 EPSRC Engineering and Physical Sciences Research Council (01-01-2024 - 31-12-2024)