Dr Mark Grant
MA (Edin), PhD (Manc)
Reader
- About
-
- Email Address
- mark.grant@abdn.ac.uk
- Telephone Number
- +44 (0)1224 273391
- Office Address
Fraser Noble Building FN137
- School/Department
- School of Natural and Computing Sciences
Biography
Dr Grant joined the University of Aberdeen as a Lecturer in 2014, having previously been a Research Associate at Durham University and a Lecturer at the Universities of Edinburgh, Nottingham and Newcastle-upon-Tyne. He was promoted to Senior Lecturer in 2018 and Reader in 2023.
- Research
-
Research Overview
Dr Grant is interested in Algebraic and Differential Topology and their applications, particularly to Robotics.
- Teaching
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- Publications
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Page 1 of 1 Results 1 to 43 of 43
Immersed but not embedded homology classes
Working Papers: Preprint PapersProjective span of Wall manifolds
Boletin Sociedad Matematica Mexicana, vol. 30, no. 3, 75Contributions to Journals: ArticlesEquivariant topological complexities
Topology and AI. European Mathematical Society Publishing House, pp. 161–186, 26 pagesChapters in Books, Reports and Conference Proceedings: Chapters (Peer-Reviewed)- [ONLINE] DOI: https://doi.org/10.4171/ESIAM/4/6
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/e4a08d7e-e4d3-4ae5-8ceb-f3f0cf887fc6/download
Projective Span of Wall Manifolds
Boletin Sociedad Matematica Mexicana, vol. 30, 75Contributions to Journals: ArticlesEquivariant topological complexities
Working Papers: Preprint PapersComparison of equivariant cohomological dimensions
Israel Journal of MathematicsContributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2302.08574
Comparison of equivariant cohomological dimensions
Working Papers: Preprint Papers- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2302.08574
- [ONLINE] BIMSA- Advances in Homotopy Theory IV Workshop
Equivariant dimensions of groups with operators
Groups, Geometry and Dynamics, vol. 16, no. 3Contributions to Journals: ArticlesParametrised topological complexity of group epimorphisms
Topological Methods in Nonlinear Analysis, vol. 60, no. 1, pp. 287-303Contributions to Journals: ArticlesIsotopy and homeomorphism of closed surface braids
Glasgow Mathematical Journal, vol. 63, no. 2, pp. 297-306Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1017/S0017089520000208
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/ba93f5cf-9284-4df7-8d31-9c94aa8fb050/download
- [ONLINE] View publication in Scopus
Topological complexity of symplectic manifolds
Mathematische Zeitschrift, vol. 295, pp. 667–679Contributions to Journals: Articles- [ONLINE] https://arxiv.org/abs/1802.04746
- [ONLINE] DOI: https://doi.org/10.1007/s00209-019-02366-x
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/a5b2f42e-060f-46e9-a39b-d32dfdd5008f/download
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/a4468bac-0ff7-4d11-b9de-40a0fcf07bba/download
- [ONLINE] View publication in Mendeley
- [ONLINE] View publication in Scopus
Equivariant dimensions of groups with operators
Working Papers: Working PapersDirected topological complexity of spheres
Journal of applied and computational topology, vol. 4, pp. 3-9Contributions to Journals: Articles- [ONLINE] http://arxiv.org/abs/1810.00339v1
- [ONLINE] DOI: https://doi.org/10.1007/s41468-019-00033-y
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/a06565d4-65af-40f9-a14e-15db588c6110/download
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/00104212-58dd-40b7-9d0d-1fb6b93693d5/download
- [ONLINE] https://www.springer.com/gp/open-access/authors-rights/self-archiving-policy/2124
- [ONLINE] View publication in Mendeley
The Topological Period-Index Conjecture for spinc 6-manifolds
Annals of K-Theory, vol. 5, no. 3, pp. 605-620Contributions to Journals: ArticlesMorita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity
Theory and Applications of Categories, vol. 35, no. 7, pp. 179-195Contributions to Journals: ArticlesHopf Invariants for sectional category with applications to topological robotics
Quarterly Journal of Mathematics, vol. 70, no. 4, pp. 1209-1252Contributions to Journals: Articles- [ONLINE] https://arxiv.org/abs/1405.6891
- [ONLINE] DOI: https://doi.org/10.1093/qmath/haz019
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/70a31884-5888-43f2-ba0f-6652004a37b9/download
- [ONLINE] View publication in Mendeley
Bredon cohomology and robot motion planning
Algebraic & Geometric Topology, vol. 19, no. 4, pp. 2023-2059Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.2140/agt.2019.19.2023
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/152ec51c-c323-4fa4-9540-cf0ee50c2f97/download
- [ONLINE] https://msp.org/publications/policies/
- [ONLINE] View publication in Scopus
Symmetrized topological complexity
Journal of Topology and Analysis, vol. 11, no. 2, pp. 387-403Contributions to Journals: Articles- [ONLINE] https://arxiv.org/abs/1703.07142
- [ONLINE] DOI: https://doi.org/10.1142/S1793525319500183
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/547fb435-1add-4fab-b1a2-a68ebe27857d/download
- [ONLINE] View publication in Scopus
- [ONLINE] View publication in Mendeley
An upper bound for topological complexity
Topology and its Applications, vol. 255, pp. 109-125Contributions to Journals: Articles- [ONLINE] https://arxiv.org/abs/1807.03994
- [ONLINE] DOI: https://doi.org/10.1016/j.topol.2019.01.007
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/9fa5664e-c9fb-4a07-bf23-8446c54ce715/download
- [ONLINE] View publication in Scopus
- [ONLINE] View publication in Mendeley
Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
Chapters in Books, Reports and Conference Proceedings: Conference ProceedingsPreface: Contemporary Mathematics
Contemporary Mathematics, vol. 702, pp. v-viiContributions to Journals: Editorials- [ONLINE] DOI: https://doi.org/10.1090/conm/702
- [ONLINE] View publication in Scopus
Topological Complexity and Related Topics: Mini-Workshop Topological Complexity and Related Topics February 28–March 5, 2016 Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany
Vol. 702, American Mathematical Society. 176 pagesBooks and Reports: BooksTopological complexity of subgroups of Artin's braid groups
Topological complexity and related topics. Grant, M., Lupton, G., Vandembroucq, L. (eds.). American Mathematical SocietyChapters in Books, Reports and Conference Proceedings: Chapters (Peer-Reviewed)- [ONLINE] http://arxiv.org/abs/1607.04830
- [ONLINE] DOI: https://doi.org/10.1090/conm/702/14105
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/bcf4f973-ad0e-4cec-9646-b52476d504b8/download
Realizing homology classes up to cobordism
Osaka Journal of Mathematics, vol. 54, no. 4, pp. 801-805Contributions to Journals: ArticlesThe Poincaré-Hopf Theorem for line fields revisited
Journal of Geometry and Physics, vol. 117, pp. 187-196Contributions to Journals: ArticlesNew lower bounds for the topological complexity of aspherical spaces
Topology and its Applications, vol. 189, pp. 78-91Contributions to Journals: ArticlesA mapping theorem for topological complexity
Algebraic & Geometric Topology, vol. 15, no. 3, pp. 1643-1666Contributions to Journals: ArticlesHomologies are infinitely complex
Topological Methods in Nonlinear Analysis, vol. 45, no. 1, pp. 55-62Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.12775/TMNA.2015.003
Sequential motion planning of non-colliding particles in Euclidean spaces
Proceedings of the American Mathematical Society, vol. 143, no. 10, pp. 4503-4512Contributions to Journals: ArticlesOn Self-Intersection Invariants
Glasgow Mathematical Journal, vol. 55, no. 2, pp. 259-273Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1017/S0017089512000481
Topological complexity of motion planning in projective product spaces
Algebraic & Geometric Topology, vol. 13, no. 2, pp. 1027-1047Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.2140/agt.2013.13.1027
On realizing homology classes by maps of restricted complexity
Bulletin of the London Mathematical Society, vol. 45, no. 2, pp. 329-340Contributions to Journals: ArticlesEquivariant topological complexity
Algebraic & Geometric Topology, vol. 12, no. 4, pp. 2299-2316Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.2140/agt.2012.12.2299
Spaces of topological complexity one
Homology, Homotopy and Applications, vol. 15, no. 2, pp. 73-81Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.4310/HHA.2013.v15.n2.a4
Self-intersections of immersions and Steenrod operations
Acta Mathematica Hungarica, vol. 137, no. 4, pp. 272-281Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1007/s10474-011-0189-9
Topological complexity, fibrations and symmetry
Topology and its Applications, vol. 159, no. 1, pp. 88-97Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1016/j.topol.2011.07.025
Topological Complexity of Configuration Spaces
Proceedings of the American Mathematical Society, vol. 137, no. 5, pp. 1841-1847Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1090/S0002-9939-08-09808-0
Topological complexity of motion planning and Massey products
Banach Center Publications, vol. 85, pp. 193-203Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.4064/bc85-0-14
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/317c64ec-e56a-4827-88e2-c4910532f189/download
Robot motion planning, weights of cohomology classes, and cohomology operations
Proceedings of the American Mathematical Society, vol. 136, no. 9, pp. 3339-3349Contributions to Journals: ArticlesBordism groups of immersions and classes represented by self-intersections
Algebraic & Geometric Topology, vol. 7, pp. 1081-1097Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.2140/agt.2007.7.1081
Symmetric Motion Planning
Chapters in Books, Reports and Conference Proceedings: Conference ProceedingsTopological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles
Chapters in Books, Reports and Conference Proceedings: Conference ProceedingsBordism Classes Represented by Multiple Point Manifolds of Immersed Manifolds
Proceedings of the Steklov Institute of Mathematics, vol. 252, no. 1, pp. 47-52Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1134/S0081543806010068
