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• Generators for various maximal and non-maximal subgroups inside the 248-dimensional irreducible adjoint representation of ${\mathrm{E}}_8(3)$:
$\mathrm{Th}$ (maximal) ${\mathrm{M}}_{10}$ ${\mathrm{L}}_3(5)$ (maximal) ${\mathrm{L}}_2(81)$ ${\mathrm{PGL}}_2(81)$ ${\mathrm{L}}_2(11)$ ${\mathrm{G}}_2(3)$ ${\mathrm{U}}_3(9)$ ${\mathrm{M}}_{11}$ ${}^3{\mathrm{D}}_4(2)$
• Generators for various Sylow subgroups of ${\mathrm{E}}_8(3)$: $2$, $5$, $7$, $11$, $13$, $41$.
• Generators for centralisers in ${\mathrm{E}}_8(3)$ for various conjugacy classes:
$2\mathrm{A}\cong {\mathrm{SL}}_2(3)\times {\mathrm{E}}_7(3{)}_{sc}$ $2\mathrm{B}\cong 2.{\mathrm{\Omega }}_{16}^{+}(3).2$ $4\mathrm{B}\cong 4.({\mathrm{\Omega }}_{14}^{-}(3).2.2)$ $4\mathrm{F}\cong 4.({\mathrm{U}}_8(3).2.2)$ $4\mathrm{G}\cong 4.(({\mathrm{U}}_4(3)\times {\mathrm{\Omega }}_{10}^{-}(3)).4)$ $5\mathrm{A}\cong 10.({\mathrm{\Omega }}_{12}^{-}(3).2)$ $5\mathrm{B}\cong 5.{\mathrm{U}}_5(9)$ $7\mathrm{A}\cong {7.}^2{\mathrm{E}}_6(3)$ $7\mathrm{B}\cong 7.{(}^3{\mathrm{D}}_4(3).{\mathrm{U}}_3(3))$ $8\mathrm{A}\cong {8.}^2{\mathrm{E}}_6(3)$ $8\mathrm{C}\cong 8.{\mathrm{\Omega }}_{12}^{-}(3).2$ $8\mathrm{E}\cong 8.({\mathrm{\Omega }}_{10}^{+}(3)\times \mathrm{Alt}(6)).2$ $8\mathrm{H}\cong 8.({\mathrm{\Omega }}_8^{-}(3)\times {\mathrm{L}}_4(3)).2$ $8\mathrm{K}\cong 8.({\mathrm{\Omega }}_8^{-}(3)\times {\mathrm{U}}_3(3)).2$ $8\mathrm{O}\cong 8.({\mathrm{L}}_4(9).4)$ $8\mathrm{P}\cong 8.({\mathrm{U}}_5(3)\times \mathrm{Alt}(6)).2$ $8\mathrm{Q}\cong 8.({\mathrm{U}}_3(3)\times {\mathrm{L}}_4(3)\times \mathrm{Alt}(6)).2$ $10\mathrm{A}\cong 10.({\mathrm{\Omega }}_{12}^{-}(3).2)$ $10\mathrm{B}\cong 20.(({\mathrm{\Omega }}_8^{+}(3)\times \mathrm{Alt}(6)){.2}^2)$ $10\mathrm{C}\cong (20.{\mathrm{PSO}}_4^{+}(3)).({\mathrm{\Omega }}_8^{-}(3).2)$ $10\mathrm{D}\cong 10.({\mathrm{U}}_4(9).2)$ $10\mathrm{E}\cong 10.({\mathrm{U}}_4(9).2)$ $10\mathrm{F}\cong 10.(({\mathrm{U}}_3(9)\times \mathrm{Alt}(6)).2)$ $11\mathrm{A}\cong 121\times {\mathrm{L}}_5(3)$ $13\mathrm{AB}\cong 13.{\mathrm{E}}_6(3)$ $13\mathrm{CD}\cong 13.{(}^3{\mathrm{D}}_4(3).{\mathrm{L}}_3(3))$ $13\mathrm{E}\cong {13}^2{\times }^3{\mathrm{D}}_4(3)$ $13\mathrm{F}\cong {13}^2\times {\mathrm{L}}_3(3{)}^2$ $14\mathrm{A}\cong 28.({\mathrm{\Omega }}_{10}^{-}(3).4)$ $14\mathrm{B}\cong (7\times {\mathrm{SL}}_2(3)).({\mathrm{U}}_6(3).2)$ $14\mathrm{C}\cong (7:(4.\mathrm{Sym}(4))){.}^3{\mathrm{D}}_4(3)$ $14\mathrm{D}\cong (7\times {\mathrm{SL}}_2(3)).({\mathrm{U}}_3(3)\times {\mathrm{L}}_2(27)).2$ $14\mathrm{E}\cong ((2\times 28).(\mathrm{Alt}(4)\times \mathrm{Sym}(4))).({\mathrm{L}}_2(27).2)$ $20\mathrm{A}\cong 40.({\mathrm{\Omega }}_{10}^{+}(3).2)$ $20\mathrm{B}\cong 20.({\mathrm{\Omega }}_{10}^{-}(3).4)$ $20\mathrm{C}\cong ({\mathrm{SL}}_2(3):40).({\mathrm{\Omega }}_8^{-}(3):2)$ $20\mathrm{D}\cong ({\mathrm{SL}}_2(3):40).({\mathrm{\Omega }}_8^{-}(3):2)$ $20\mathrm{E}\cong 20.(({\mathrm{L}}_4(3)\times {\mathrm{U}}_4(3)).4)$ $20\mathrm{F}\cong (2\times 20).((\mathrm{Alt}(6)\times {\mathrm{U}}_4(3))).(2\times 4)$ $20\mathrm{G}\cong (2\times 20).((\mathrm{Alt}(6)\times {\mathrm{U}}_4(3))).(2\times 4)$ $20\mathrm{H}\cong {\mathrm{Q}}_8.(40\times 3:4).({\mathrm{L}}_4(3).2)$ $20\mathrm{I}\cong {\mathrm{Q}}_8.(2\times 60).2.({\mathrm{U}}_4(3):4)$ $20\mathrm{J}\cong (4\times 80).({\mathrm{U}}_4(3):4)$ $20\mathrm{K}\cong 80\times {\mathrm{U}}_3(9)$ $20\mathrm{L}\cong (10\times 20).({\mathrm{L}}_4(3):2)$ $20\mathrm{M}\cong 2.{\mathrm{Q}}_8^2.6\times 6.60.2.(\mathrm{Alt}(6):2)$ $20\mathrm{N}\cong {\mathrm{Q}}_8.(10\times 3:4).{\mathrm{L}}_2(81)$ $20\mathrm{O}\cong 80.({\mathrm{L}}_2(81):2)$ $20\mathrm{P}\cong (10\times 80).(\mathrm{Alt}(6):2)$ $22\mathrm{A}\cong 242.({\mathrm{L}}_4(3):2)$ $22\mathrm{B}\cong 121\times {\mathrm{GL}}_2(3)\times {\mathrm{L}}_3(3)$ $26\mathrm{AB}\cong 26.({\mathrm{\Omega }}_{10}^{+}(3).2)$ $26\mathrm{CD}\cong (13\times {\mathrm{SL}}_2(3)).({\mathrm{L}}_6(3).2)$ $26\mathrm{EF}\cong (13\times {\mathrm{GL}}_2(3)){.}^3{\mathrm{D}}_4(3)$ $26\mathrm{GH}\cong (13\times {\mathrm{SL}}_2(3)).({\mathrm{L}}_2(27)\times {\mathrm{L}}_3(3):2)$ $26\mathrm{IJ}\cong {\mathrm{Q}}_8.(39\times {\mathrm{Q}}_8).6.({\mathrm{L}}_2(27):2)$ $26\mathrm{K}\cong ({13}^2\times {\mathrm{SL}}_2(3)).({\mathrm{L}}_2(27):2)$ $26\mathrm{LM}\cong {13}^2\times {\mathrm{GL}}_2(3)\times {\mathrm{L}}_3(3)$ $26\mathrm{N}\cong {\mathrm{Q}}_8^2{.3}^2.13.26.2$ $35\mathrm{A}\cong 280.({\mathrm{L}}_4(3).2)$ $41\mathrm{AE}\cong 82.({\mathrm{\Omega }}_8^{-}(3).2)$ $41\mathrm{FJ}\cong 82.({\mathrm{L}}_2(81).2)$ $41\mathrm{KO}\cong 2^2\times {41}^2$
• Generators for various conjugacy classes of maximal subgroups inside the 78-dimensional representation of ${}^2{\mathrm{E}}_6(2)$:
${\mathrm{F}}_4(2)$ (3 classes) $2^2{.2}^9{.2}^{18}:({\mathrm{L}}_3(4)\times \mathrm{Sym}(3))$ ${\mathrm{Fi}}_{22}$ (3 classes) ${\mathrm{\Omega }}_{10}^{-}(2)$ $\mathrm{Sym}(3)\times {\mathrm{U}}_6(2)$ $(3\times {\mathrm{\Omega }}_8^{+}(2)):3):2$ $3^{1+6}{.2}^{3+6}.(\mathrm{Sym}(3)\times 3)$ $3^2{\mathrm{Q}}_8\times {\mathrm{U}}_3(3):2$

Publications

• Javed, M., Parkin, J., Rowley, P., & Walton, J., The Maximal Tori of Finite Exceptional Groups of Lie Type, Communications in Algebra, 2024. (linked here).

Teaching

• MATH10111 - Foundations of Pure Mathematics
• MATH11112 - Real Analysis
• MATH11221 - Mathematical Problem Solving
• MATH19681 - Mathematics 1E1
• MATH19861 - Mathematics 0N1
• MATH42121 - Galois Theory
• MATH11022 - Linear Algebra
• MATH20622 - Progamming with Python

• Mathematical Modelling Day - leading a interactive workshop on the mathematics of card shuffling in 2022, 2023 and 2024. All hosted at The University of Manchester.
• Problem Solving Matters Event - Hosted at The University of Manchester in 2022.
• Maths in the Real World Event - Hosted at The University of Manchester in 2022.