# Dr Andrew Morris BSc (Hons) PhD

School of Mathematics

Associate Professor in Mathematical Analysis

## Contact details

- 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.*

## 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**

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):to appear.

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: http://www.ams.org/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. London 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. London 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.

eprints: arxiv.org/find/math/1/au:+Morris_Andrew/0/1/0/all/0/1