Mathematician · Research Fellow
Aluna
Rizzoli
I study algebraic groups through the way they act — orbit structures, dense orbits, and generic stabilizers — in the geometry group at King’s College London.
01 / about
A mathematician who codes the abstract into the concrete.
I am a Postdoctoral Fellow in the geometry group at King’s College London, working on algebraic groups, rational actions, and representation theory.
I completed my PhD at Imperial College London under Martin Liebeck, followed by a year as an INI–Simons Postdoctoral Fellow at the University of Cambridge and two years as an SNSF-funded Research Scientist at EPFL.
// experience & education
- 2024–Research FellowKing’s College London — geometry group
- 2022–24Research Scientist (SNSF)EPFL — Testerman group
- 2021–22INI–Simons Postdoctoral FellowUniversity of Cambridge
- 2017–21PhD in MathematicsImperial College London — “A double coset problem for classical groups”, adv. Martin Liebeck
- 2013–17MMath, 97.0% · Miller PrizeUniversity of St Andrews
Selected talks at Imperial, Manchester, Warwick, Cambridge, EPFL, Banff, and others. Awards include the EPSRC Studentship, Miller Prize, Sanderson Prize, and the Arthur Hinton Read Memorial Prize.
02 / research
Algebraic groups, studied through their actions.
I study algebraic groups indirectly — through the way they act on other objects, and what their orbit structures reveal. A lot of my work is computational: I write Magma code to understand the actions of matrix groups over finite fields, then connect the results back to the infinite case.
My recent work classifies the generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians, and explores multiplicity-free representations and modules with finitely many orbits.
03 / publications
Selected publications
7 papers · 2017–2025
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Draft
On the inverse problem for isometry groups of finite-dimensional norms
In preparation — a proof of a 40-year-old open problem.
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2025
Multiplicity-free representations of the principal A₁-subgroup in a simple algebraic group
Pacific Journal of Mathematics — vol. 336
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2025
Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians
Forum of Mathematics, Sigma — vol. 13
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2022
Modules for algebraic groups with finitely many orbits on totally singular 2-spaces
Journal of Algebra — vol. 606
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2021
Finite singular orbit modules for algebraic groups
Journal of Algebra — vol. 570
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2018
On the average box dimensions of graphs of typical continuous functions
Acta Mathematica Hungarica — vol. 156
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2017
Interactive simulations for quantum key distribution
European Journal of Physics — vol. 38, no. 3
04 / side projects
Data science & machine learning, for fun
Written up on Medium
//01
Jailbreaking ChatGPT’s image generator
Probing the limits of OpenAI’s safety layer for DALL·E 3 using recursive complexity and evasive language.
Read on Medium ↗//02
Predicting chess results with LightGBM
Gradient-boosted models trained on Lichess data that out-predict the Glicko-2 rating system.
Read on Medium ↗//03
Adding a 4-point line to the NBA
Using the NBA API to find which games across 20 seasons would have flipped with a 30-foot 4-point line.
Read on Medium ↗05 / beyond the math
Off the page
When I’m not chasing orbits, I play chess, explore London’s theatre scene, and keep up an ongoing (and stubbornly difficult) sourdough journey.
06 / contact
Get in touch.
aluna.rizzoli@kcl.ac.uk Department of MathematicsKing’s College London
Strand, London WC2R 2LS
United Kingdom