Mathematics · King’s College London
Teaching mathematics and physics, and exploring the algebraic structures that connect symmetry, gravity and fundamental theory.
Profile
About
I am Paul P. Cook, a mathematician and educator at King’s College London. My work sits at the meeting point of algebra, geometry and theoretical physics, with a particular interest in the deep symmetries underlying gravity and extended objects.
Alongside research, I teach across mathematics and physics. I aim to make demanding ideas precise without losing the intuition that makes them meaningful — whether in a first encounter with calculus or an MSc research project.
Career
Academic appointments
Current position · from August 2025
Grade 8 · King’s College London
Teaching across mathematics and physics, supervising postgraduate work, contributing to education leadership, and continuing research in algebraic approaches to fundamental physics.
King’s College London
An extended teaching-focused appointment encompassing curriculum development, undergraduate assessment, project coordination, tutor leadership and teaching across mathematics and mathematical physics.
Fixed-term appointment · King’s College London
A teaching-intensive role combining lectures and tutorials with widening participation, student support and the development of mathematics education and communication activity.
Fixed-term appointment · King’s College London
Undergraduate and MSc teaching in areas including dynamics, manifolds and foundations of mathematical physics, alongside research and postgraduate supervision.
Scuola Normale Superiore di Pisa
A two-year fellowship within the European Superstring Theory Network (MRTN-CT-2004-512194), working on “Symmetries of M-theory” with the groups of Augusto Sagnotti and Massimo Bianchi.
Teaching
Teaching & learning
My teaching combines clear, staged explanations with historical and physical context. Detailed lecture notes are part of that practice: a durable route into the subject, not a separate activity from the classroom.
Principal & recent lecturing
Special Relativity & Electromagnetism2020–26
Groups & Symmetries2017–26
Introductory Quantum Theory2024–25
Calculus I2013–20
Earlier lecturing
Intermediate Dynamics2008–13
Foundations of Mathematical Physics2011–13
Manifolds2009–11
Mechanics, Relativity & Quantum Theory2010–11
Beyond the lecture theatre
Research supervisionPhD, MSc/MSci, BSc and vacation-bursary projects in mathematics and mathematical physics.
Course & curriculum designDesigned Foundations of Mathematical Physics; reshaped Calculus I, Groups & Symmetries, and Special Relativity & Electromagnetism.
Departmental educationUndergraduate project coordination, exam-board work, curriculum review and leadership of the department’s graduate teaching assistants.
The teaching library
Six substantial sets of notes document current, recent and historical teaching. Together they span calculus, symmetry, mechanics, relativity, electromagnetism and quantum theory.
A full course text moving from vector calculus and electrostatics through electrodynamics, relativity and field theory.
Paul P. Cook
Open PDFFrom old quantum theory and wave mechanics to the operator and Hilbert-space formulation and core quantum systems.
P. Kravchuk, N. Lambert, G. Watts, P.P. Cook and others
Open PDFGroups, permutations, cosets, homomorphisms, group actions and matrix-group structure, developed with worked examples.
G. Papadopoulos, B. Doyon, P.P. Cook and others
Open PDFA broad foundation in classical mechanics, relativity, quantum mechanics and the role of group theory in physics.
Paul P. Cook
Open PDFNotes on vectors, motion, rotating systems, forces, and Lagrangian and Hamiltonian mechanics.
Paul P. Cook
Open PDFA complete course text on functions, limits, differentiation, integration, power series and tutorial exercises.
Paul P. Cook
Open PDFEdition noteThese are dated teaching resources. Current module information and guidance take precedence.
Talks
Public engagement
A selected archive of talks for schools, maths clubs, undergraduate audiences and research colleagues.
A route from familiar geometric symmetry through braids and knots to some of the vast structures encountered in modern group theory.
Open slidesSpace-time diagrams, time dilation and length contraction developed through several celebrated relativistic puzzles.
Open slidesDispersion, breaking waves, shallow-water solitons and the KdV equation, with examples drawn from physical wave phenomena.
Open slidesA journey from rotating and inertial frames to the changes in our understanding of space and time brought by relativity.
Open slidesHandwritten notes developing continuous symmetry, Lie brackets, roots and the structure of semisimple Lie algebras. These are the complete source notes for the talk.
Open handwritten notesKac–Moody root systems, E₁₁ decompositions and one- and two-parameter families of M-theory solutions.
Open slidesTaking its title from Schrödinger’s famous remark, this blackboard journey moves from the double-slit experiment and wave–particle duality through the Schrödinger equation, measurement and entanglement to the Elitzur–Vaidman bomb tester.
Open blackboard notesArchive noteThese are dated versions of talks as delivered. Current presentations may be revised, and embedded animations or media may not play in the PDF editions.
Podcasts
AI-generated audio series
Three curated series of Gemini Notebook Audio Overviews, offering guided introductions to topics in mathematical physics.
Production noteThese podcasts are AI-generated Audio Overviews produced with Google’s Gemini Notebook, formerly NotebookLM, and curated by Paul P. Cook.
Open the complete listening pageResearch
Research interests
My published research seeks to clarify the physical role of E₁₁ and related Kac–Moody algebras: from brane solutions and charge multiplets, through gravitational cosets and Hodge dualities, to higher dualisations of linearised gravity and the recent unfolding of E₁₁.
Follow the published recordSelected published trajectory
Brane solutions, charge multiplets and bound states within exceptional Kac–Moody frameworks.
↗2012–14Gravity & dualityOff-shell Hodge dualities and gravitational coset models linking algebra to spacetime fields.
↗2022Higher dualisationsLinearised gravity and the infinite tower organised by the A₁⁺⁺⁺ algebra.
↗2025Unfolding E₁₁Fields, dual fields and higher duals in a systematic exceptional-algebraic description.
↗Visualisations by Paul P. Cook, generated from the A₁₀ decomposition of E₁₁ using SimpLie, software created by Teake Nutma.
Papers
Research publications
Research spanning exceptional symmetry, gravity, branes and Kac–Moody structures. Links open the corresponding arXiv record wherever one exists.
Paul P. Cook · Sarben Sarkar
Physica Scripta (2026)Nicolas Boulanger · Paul P. Cook · Josh A. O’Connor · Peter West
SciPost Physics 18, 149 (2025)Nicolas Boulanger · Paul P. Cook · Josh A. O’Connor · Peter West
Journal of High Energy Physics 12, 152 (2022)Paul P. Cook · Michael Fleming
Journal of High Energy Physics 07, 115 (2014)Nicolas Boulanger · Paul P. Cook · Dmitry Ponomarev
Journal of High Energy Physics 09, 089 (2012)Paul P. Cook
Journal of High Energy Physics 03, 028 (2012)Paul P. Cook
Classical and Quantum Gravity 26, 235023 (2009)Paul P. Cook · Peter West
Journal of High Energy Physics 11, 091 (2008)Paul P. Cook
Nuclear Physics B Proceedings Supplements 171, 271–274 (2007)Paul P. Cook · Peter West
Journal of High Energy Physics 12, 041 (2005)Paul P. Cook · Peter West
Nuclear Physics B 705, 111–151 (2005)Interests
Current research interests
Broad areas in which I welcome conversations with researchers and students. They are intentionally expansive and offered as starting points for discussion.
Exceptional and very-extended Kac–Moody algebras as organising structures for M-theory, string theory and supergravity.
Algebraic descriptions of branes and gravitational solutions, together with mixed-symmetry fields, Hodge duality, compactification and U-duality.
Representation-theoretic approaches to large symmetry algebras, including operator, oscillator and Fock-space viewpoints and their physical interpretation.
The geometry and physical meaning of extended and exotic coordinates, and their relationship to fields, higher duals and spacetime symmetry.
Broader questions involving Lie superalgebras, W-algebras and conformal structures, integrability and Dunkl-type operators in mathematical physics.
Structural questions arising from relativistic and non-Lorentzian symmetry, including Carrollian limits and related geometric frameworks.
Research conversationsI welcome exploratory discussion across these areas and their connections to mathematical physics.
Contact
Get in touch
Affiliation
Department of Mathematics