# Supervision and Teaching

Since 2020, I have been a Fellow of the Higher Education Academy, and for my dedication to teaching and learning, in 2018, I was honoured to have received the Terrance Harris Excellence in Mentorship Award from California Polytechnic State University.

I have held several leadership roles at the University of Birmingham, for instance, from 2022 to 2024, I led the Topology and Dynamics Research Group, in the academic year 2023/24, I chaired the School of Mathematics’ Information Technology and Digital Delivery Committee, and from 2020 to 2023, I was a Director of Student Experience.

Below is a selection of research projects and dissertations I have supervised as well as a list of lecture courses I have taught. Enquiries from potential postdoctoral researchers, as well as research students and visitors, are always welcome.

## Supervision

- Postdoctoral research projects supervised and co‑supervised.
*Ultrasound signal analysis for diagnosing and predicting battery cell defects*(current).*Complexity of random substitution tilings*(2023-2024).*Deciphering the 3D structure of the epigenome for cancer diagnostics*(2021-2022).*Rauzy fractals of random substitutions*(2019-2020).

- Doctoral supervision and co‑supervision.
*Discrete and continuous aspects of Lipschitz mappings*(current).*Fractal Martin boundaries*(current).*Morphology of mitochondria in breast cancer cells*(current)*Preservation of shadowing by factor maps*(current).*Random β-transformations*(current).*Topological games and dimensionality*(current).*Complexity of dynamical systems arising from random substitutions*(2019-2023).*Finite and infinite rotation sequences and beyond*(2015-2019).*Measure–geometric Laplacians on the real line*(2014-2018).*Regularity of aperiodic subshifts*(2014-2018).

- Masters dissertations supervised and co‑supervised.
*An investigation into Schmidt games*(2023-2024).*Hilbert’s curve and its friends*(2020-2021).*Space filling curves*(2019-2020).*Annihilating continued fractions*(2017-2018).*Intermediate β–shifts of finite type*(2017-2018).*The mass transference principle*(2017-2018).*Fractals as Martin boundaries*(2015-2016).*Entropy of the 1d–Greenberg–Hastings model*(2014-2015).*Hausdorff dimension of graphs of Weierstrass functions*(2014-2015).*Spectral asymptotics of measure geometric Laplacians*(2013-2014).*Diffusion on nested fractals*(2013-2014).

- Undergraduate dissertations supervised and co‑supervised.
*A brief history of cryptography*(2022-2023).*A study into the aerodynamics of performance cars*(2022-2023).*A study of Sudoku*(2022-2023).*Game ranking systems*(2022-2023).*How long is a piece of string: A paradox of length*(2022-2023).*Leonhard Euler and the five room puzzle*(2022-2023).*Modelling stock market volatility with GARCH-type models*(2022-2023).*Panel data regression analysis and its applications*(2022-2023).*An introduction to fractal geometry*(2015-2016).*Chacon–Ornstein ergodic theorem and applications*(2013-2014).

- Undergraduate research projects supervised and co‑supervised.
*Mathematics and music*(2023).*Portfolio analysis*(2022).*Continuity of entropy of Lorenz maps*(2017).*Counterexamples in analysis*(2017).*Space filling curves and turtle walks*(2017).

## Lecture courses

- University of Exeter, UK.
- MTH3040:
*Topology and Metric Spaces*.

- MTH3040:
- University of Birmingham, UK.
- 2 MVA:
*Multivariable and vector analysis*.

- 2 MVA:
- California Polytechnic State University, USA.
- Universität Bremen, Germany.
*Fractal geometry*.*Markov chains*.

- University of St Andrews, UK.
- MT 1003:
*Pure and applied mathematics*.

- MT 1003:

## Tutoring and demonstrating

- University of Exeter, UK.
- MTH2008:
*Real Analysis*.

- MTH2008:
- University of Birmingham, UK.
- 1 PS:
*Probability and statistics*.

- 1 PS:
- University of St Andrews, UK.
- Postgraduate:
*SMSTC Analysis*. - Postgraduate:
*SMSTC Geometry and topology*. - MT 5865:
*Measure and ergodic theory*. - MT 3501:
*Linear algebra*. - MT 2005:
*Discrete mathematics*. - MT 2002:
*Algebra and analysis*. - MT 1003:
*Pure and applied mathematics*.

- Postgraduate: