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.

Available PhD opportunities

• From dynamics to number theory: Further details available here.

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.
• University of Birmingham, UK.
  • 2 MVA: Multivariable and vector analysis.
• California Polytechnic State University, USA.
  • Math 142: Calculus II.
  • Math 143: Calculus III.
  • Math 206: Linear algebra I.
  • Math 306: Linear algebra II.
  • Math 440 and Math 540: Topology I.
  • Math 441 and Math 541: Topology II.
  • Math 550: Real analysis.
• Universität Bremen, Germany.
  • Fractal geometry.
  • Markov chains.
• University of St Andrews, UK.
  • MT 1003: Pure and applied mathematics.

Tutoring and demonstrating

• University of Exeter, UK.
  • MTH2008: Real Analysis.
• University of Birmingham, UK.
  • 1 PS: Probability and statistics.
• 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.