I am a BMS Dirichlet fellow (postdoc) in the Nonsmooth Variational Problems and Operator Equations group at the Weierstrass Institute in Berlin.

I work on the numerical solution of partial differential equations, with a particular focus on

- high-order spectral/hp-finite element methods,
- topology optimization,
- quasivariational inequalities,
- computing multiple solutions of nonlinear PDEs.

I have applied the numerical techniques I develop to various applications, in the areas of fractional PDEs and topology optimization.

I lead the development of fir3dab, and regularly commit to Julia packages in JuliaApproximation.

I have collected a number of self-contained codes in MATLAB, Python, and Julia of deflation techniques for computing multiple solutions of nonlinear discretized PDEs/systems in a Github repository.

## Noteable Prizes

- IMA Leslie Fox Prize in Numerical Analysis, second place (2023).
- Durham Prize, awarded by Keble College for performance during an MSc (2017).
- Gerald Whitrow Prize, awarded for excellence during the final undergraduate examinations (2016).
- Dean’s List, awarded to the top 10% of the cohort (2016).
- London Mathematical Society undergraduate research bursary (2015).

## News

21 Feb 2024: I gave a talk in the Weierstrass Institute seminar on Non-smooth Variational Problems and Operator Equations in Berlin, Germany, on computing multiple solutions of topology optimization problems. Click for slides.

21 Feb 2024: Sheehan Olver and I submitted a manuscript entitled "A sparse hierarchical hp-finite element method on disks and annuli" (arXiv).

20 Feb 2024: Kars Knook, Sheehan Olver and I submitted a manuscript entitled "Quasi-optimal complexity hp-FEM for Poisson on a rectangle" (arXiv).

29 Nov 2023: A paper was published in SISC on "Preconditioners for Computing Multiple Solutions in Three-Dimensional Fluid Topology Optimization" together with Patrick Farrell (DOI: 10.1137/22M1478598).

22 Nov 2023: Timon S. Gutleb, José A. Carrillo, Sheehan Olver and I submitted a manuscript entitled "A frame approach for equations involving the fractional Laplacian" (arXiv).

21 Nov 2023: Timon S. Gutleb and I submitted a manuscript entitled "Explicit fractional Laplacians and Riesz potentials of classical functions" (arXiv).

15 Nov 2023: I moved to Berlin and I am now a BMS Dirichlet postdoctoral fellow based in the Weierstrass Institute.

13 Oct 2023: I gave a talk in the numerical analysis seminar at the University of Bath, UK. I spoke on a sparse hp-finite element method for the Helmholtz equation posed on disks, annuli, and cylinders.

11 Oct 2023: Timon S. Gutleb, Richard M. Slevinsky, Sheehan Olver and I submitted a manuscript entitled "Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli" (arXiv).

10 Oct 2023: I gave a talk in the internal numerical analysis seminar at the University of Oxford, UK. I spoke on a sparse hp-finite element method for the Helmholtz equation posed on disks, annuli, and cylinders.

25 Sep 2023: I gave a talk in the EUCCO 2023 conference in Heidelberg, Germany, on computing multiple solutions of topology optimization problems. Click for slides.

24 Aug 2023: I gave a talk in ICIAM 2023 in Tokyo, Japan, on sparse spectral methods for fractional PDEs. Click for slides.

14 Aug 2023: I gave a talk in the Numerical Analysis in the 21st Century conference in honour of Nick Trefethen's retirement from Oxford. I spoke on sparse hp-FEM and SEM for the Helmholtz equation posed on disks and annuli.

24 Jul 2023: I gave a talk in the USNCCM17 conference in Albuquerque, New Mexico, on computing multiple solutions of topology optimization problems. Click for slides.

17-21 Jul 2023: I visited Dan Fortunato in the Flatiron Institute in NYC and gave a talk on sparse hp-FEM methods for the Helmholtz equation.

29 Jun 2023: I gave a talk in the 29th Biennial Numerical Analysis Conference in Strathclyde, Glasgow, on sparse spectral methods for fractional PDEs. Click for slides.

29-30 Jun 2023: I co-organised a minisymposium of 12 speakers (together with Timon Gutleb and Marco Fasondini) on "Spectral methods and orthogonal polynomials" in the 29th Biennial Numerical Analysis Conference in Strathclyde, Glasgow.

26 Jun 2023: I won second place in the Leslie-Fox prize competition. Click for slides.

2 Mar 2023: I gave a talk in CSE23 in Amsterdam, Netherlands, on sparse spectral methods for fractional PDEs. Click for slides.

2 Mar 2023: I organised a minisymposium of 8 speakers on "Applications & Implementations of Fast Spectral Methods" in CSE23 in Amsterdam, Netherlands.

16 Nov 2022: I gave a talk in the IC-UCL numerical analysis seminar at UCL, UK, on the numerical analysis of a topology optimization problem for the compliance of a linearly elastic structure.

20 Oct 2022: I was an invited speaker in the Applied Mathematics seminar in Leicester University, UK and spoke on sparse spectral methods for fractional PDEs. Click for slides.

20 Sep 2022: I gave a talk in the second numerical analysis and acoustics workshop, held at Imperial College London, on sparse spectral methods for fractional PDEs. Click for slides.

15 Aug 2022: I gave a talk in the GAMM 2022 conference in Aachen, Germany on computing multiple solutions of topology optimization problems as part of a Young Researchers Minisymposium. Click for slides.

19 Jul 2022: I gave an invited talk in the PDE CDT reunion conference in Oxford, UK, on sparse spectral methods for fractional PDEs. Click for slides.

7 Dec 2021: I received my Leave to Supplicate from the University of Oxford. I officially hold a DPhil (PhD).

24 Sep 2021: I passed my DPhil (PhD) viva with minor corrections!

1 Jul 2021: I have started as a research assistant at Imperial College London working in the group of Dr Sheehan Olver.