Article

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, He, Yang-Hui, Heyes, Elli and Hirst, Edward (2022) Cluster Algebras: Network Science and Machine Learning. arXiv.

Farzad, Fatehi, Bingham, Richard, Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Stockley, Peter and Twarock, Reidun (2021) Therapeutic Interfering Particles Exploiting Viral Replication and Assembly Mechanisms Show Promising Performance: A Modelling Study. Scientific Reports, 11 (23847).

Fatehi, Farzad, Bingham, Richard J., Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Stockley, Pete G. and Twarock, Reidun (2021) Therapeutic Interfering Particles Exploiting Viral Replication and Assembly Mechanisms Show Promising Performance: A Modelling Study. arXive.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2021) Clifford spinors and root system induction: H4 and the Grand Antiprism. Advances in Applied Clifford Algebras, 31 (57).

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 and He, Yang-Hu (2021) Machine-learning a virus assembly fitness landscape. PLOS ONE, 16 (5). e0250227.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 and Twarock, Reidun (2021) Models of viral capsid symmetry as a driver of discovery in virology and nanotechnology. The Biochemist, 43 (1). pp. 20-24.

Twarock, Reidun, Stockley, Peter G., Bingham, Richard J., Dykeman, Eric C. and Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2020) Conservation of Genetically-Embedded Virus Assembly Instructions: A Novel Route to Antiviral Therapy. Proceedings, 50 (1). p. 87.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2018) From the Trinity $(A_3, B_3, H_3)$ to an $ADE$ correspondence. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2220).

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) The E8 Geometry from a Clifford Perspective. Advances in Applied Clifford Algebras, 27 (1). pp. 397-421.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) Clifford Algebra is the Natural Framework for Root Systems and Coxeter Groups. Group Theory: Coxeter, Conformal and Modular Groups. Advances in Applied Clifford Algebras, 27 (1). pp. 17-31.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) Root systems & Clifford algebras: from symmetries of viruses to E8 & ADE correspondences. Conference Series- Institute of Physics. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) A novel conformal geometric algebraic construction of the modular and braid groups. Journal of Mathematical Physics. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) A 3D Spinorial View of 4D Exceptional Phenomena. Symmetries in Graphs, Maps, and Polytopes. pp. 81-95.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) The birth of E8 out of the spinors of the icosahedron. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2185).

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2015) Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction. Journal of Physics: Conference Series, 597.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Nature Physics Research Highlight: Know your onions. Nature Physics, 10 (1). p. 244.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Wardman, Jess, Keef, Thomas and Twarock, Reidun (2014) Viruses and Fullerenes - symmetry as a common thread? Acta Crystallographica Section A: Foundations and Advances, 70 (Pt 2). pp. 162-167.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) A Clifford Algebraic Framework for Coxeter Group Theoretic Computations. Advances in Applied Clifford Algebras, 24 (1). pp. 89-108.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2013) Platonic solids generate their four-dimensional analogues. Acta Crystallographica Section A: Foundations and Advances, 69 (6). pp. 592-602.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Bœhm, Céline and Twarock, Reidun (2013) Affine extensions of non-crystallographic Coxeter groups induced by projection. Journal of Mathematical Physics, 54 (21). pp. 1-22.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2013) Clifford Algebra Unveils a Surprising Geometric Significance of Quaternionic Root Systems of Coxeter Groups. Advances in Applied Clifford Algebras, 23 (2). pp. 301-321.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Bœhm, Céline and Twarock, Reidun (2012) Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups. Journal of Physics A: Mathematical and Theoretical, 45 (28).

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Lasenby, Anthony and Hobson, Michael (2010) Cracking the Taub-NUT. Classical and Quantum Gravity, 27 (18).

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Lasenby, Anthony and Hobson, Michael (2009) Anisotropic, nonsingular early universe model leading to a realistic cosmology. Physical Review D, 79 (4).

Book Section

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2022) A sheep in wolf’s clothing: from group theory to a novel antiviral strategy. In: Nankai Symposium on Mathematical Dialogues: Celebrating the 110th anniversary of the birth of Prof. S.-S. Chern. Springer

Monograph

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010, Konovalov, Alexander and Lelievre, Samuel (2017) Software Carpentry: Programming with Sage. Working Paper. UNSPECIFIED. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) A systematic construction of representations of quaternionic type for the polyhedral groups. Working Paper. University of York. (Unpublished)

Conference or Workshop Item

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2021) Viruses, polytopes and machine learning. In: Nankai Symposium on Mathematical Dialogues, 2-13 August 2021, Chern Institute of Mathematics, Nankai University, Tianjin, China (via Zoom).

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2020) Mathematical and computational modelling in Mathematical Virology. In: Plymouth Maths, 3rd December 2020, Plymouth. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2019) Machine-learning a virus assembly fitness landscape. In: SIAM Conference on Applied Algebraic Geometry, 9th - 13th July 2019, University of Bern, Bern, Switzerland. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2018) Recent developments in mathematical virology. In: Nonlinear Algebra in Applications, 12th - 16th November 2018, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) A Clifford algebraic approach to reflection groups and root systems. In: Yau Institute Seminar in Geometry and Physics, 10th August 2017, Yau Mathematical Sciences Center (YMSC), Tsinghua, China. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) Root systems & Clifford algebras: from symmetries of viruses to E8 & ADE correspondences. In: Chern Institute: Nankai Symposium on Physics, Geometry and Number Theory, 30th July - 5th August 2017, Tianjin, China. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2017) Root systems & Clifford algebras: from symmetries of viruses to E8 & an ADE correspondence. In: Pure Mathematics Colloquium, 13th January 2017, University of St Andrews, Scotland. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) Root systems and Clifford algebras: from symmetries of viruses to E8 and an ADE-like correspondence. In: Colloquium talk, 6th December 2016, City University, London. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) A conformal geometric algebra construction of the modular group. In: Alterman Conference on Geometric Algebra, 1st - 9th August 2016, Brasov, Romania. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) A systematic construction of representations of quaternionic type. In: Alterman Conference on Geometric Algebra, 1st - 9th August 2016, Brasov, Romania. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) A new take on polyhedral things. In: Applied Algebra, 3rd June 2016, Oxford University. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) A 3D spinorial view of the exceptional root systems. In: Integrable Systems in Newcastle, 5th - 6th February 2016, Northumbria University, Newcastle upon Tyne. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2016) A new construction of E8 and the other exceptional root systems. In: Algebra Seminar, 18th January 2016, Queen Mary University of London. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2015) A Clifford algebraic construction of the E8 root system. In: Yau Institute: Tsinghua Summer Workshop in Geometry and Physics 2017, 6-12 Aug 2017, Yau Institute, Tsinghua University, Beijing, China. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2015) The E8 geometry from a Clifford perspective. In: The 6th Conference on Applied Geometric Algebras in Computer Science and Engineering, 29-31 July 2015, Universitat Politècnica de Catalunya, Barcelona, Spain. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2015) Surprises in icosahedral symmetry. In: Mathematics Seminar, 6th May 2015, Northumbria University, Newcastle upon Tyne. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Affinne symmetry principles for non-crystallographic systems & applications to viruses/carbon onions. In: Mathematics Seminar, 16th December 2014, Doppler Institute, Technical University, Prague. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) A 3D spinorial view of 4D exceptional phenomena. In: Mathematics Seminar, 12th December 2014, Charles University, Prague. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Platonic solids generate their four-dimensional analogues - a 3D spinorial view of 4D exceptional phenomena. In: Algebra Seminar, 17th November 2014, University of York. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Platonic solids generate their four-dimensional analogues - a 3D spinorial view of 4D exceptional phenomena. In: Mathematical Sciences Seminar - Rank 3 root systems/Coxeter groups induce (the exceptional) rank 4 root systems/Coxeter groups via a new Clifford spinor construction, 10th November 2014, Birkbeck, University of London. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Platonic solids generate their four-dimensional analogues - a 3D spinorial view of 4D exceptional phenomena. In: 10th International Conference on Clifford Algebras and their Applications in Mathematical Physics, 4th – 9th August 2014, Tartu, Estonia. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Affine symmetry principles for non-crystallographic systems & applications to viruses/carbon onions. In: 30th International Colloquium on Group Theoretical Methods in Physics, 14th - 18th July 2014, Ghent University, Ghent, Belgium. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Platonic solids generate their four-dimensional analogues. In: 5th Workshop SIGMAP - Symmetries In Graph, Maps And Polytopes, 7th - 11th July 2014, ELIM Conference Centre, West Malvern. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) Recent developments in affine symmetry principles for non-crystallographic systems. In: Open Statistical Physics Annual Meeting, 26th March 2014, Open University, Milton Keynes. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2014) What Clifford algebra can do for Coxeter groups and root systems. In: Maths HEP Lunchtime Seminar, 21st February 2014, Durham University. (Unpublished)

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 (2012) A Clifford Algebraic Framework for Coxeter Group Theoretic Computations. In: Applied Geometric Algebras in Computer Science and Engineering, 2-4 July 2012, La Rochelle, France.

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 A Clifford perspective on reflection groups, root systems and ADE correspondences. In: 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics, 3-7 August 2020, University of Science and Technology of China, University of Science and Technology of China. (Unpublished)

Other

Dechant, Pierre-Philippe ORCID: https://orcid.org/0000-0002-4694-4010 and He, Yang-He (2019) Machine-learning a virus assembly fitness landscape. arXive. (Unpublished)