Dr Mark Grant
MA (Edin), PhD (Manc)
Reader
- 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 Overview
Dr Grant is interested in Algebraic and Differential Topology and their applications, particularly to Robotics.
Page 1 of 1 Results 1 to 42 of 42
Equivariant topological complexities
Grant, M.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/bitstream/2164/24970/1/Grant_EquivariantTC.pdf
Projective Span of Wall Manifolds
Grant, M., Schutte, B.Boletin Sociedad Matematica Mexicana, vol. 30, 75Contributions to Journals: ArticlesProjective span of Wall manifolds
Schutte, B. P., Grant, M.Boletin Sociedad Matematica Mexicana, vol. 30, 75Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1007/s40590-024-00648-x
Equivariant topological complexities
Grant, M.Working Papers: Preprint Papers- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2402.01540
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/23167/1/2402.01540v1.pdf
Comparison of equivariant cohomological dimensions
Grant, M., Li, K., Meir Ben Efraim, E., Patchkoria, I.Israel Journal of MathematicsContributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2302.08574
Comparison of equivariant cohomological dimensions
Grant, M., Li, K., Meir, E., Patchkoria, I.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
Grant, M., Meir, E., Patchkoria, I.Groups, Geometry and Dynamics, vol. 16, no. 3Contributions to Journals: Articles- [ONLINE] https://arxiv.org/pdf/1912.01692.pdf
- [ONLINE] DOI: https://doi.org/10.4171/GGD/686
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/20122/2/Grant_EquivariantDimensionsOfGroupsWithOperators_VOR.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/20122/1/Grant_GGD_EquivariantDimensionsOf_AAM.pdf
Parametrised topological complexity of group epimorphisms
Grant, M.Topological Methods in Nonlinear Analysis, vol. 60, no. 1, pp. 287-303Contributions to Journals: ArticlesIsotopy and homeomorphism of closed surface braids
Grant, M., Sienicka, A.Glasgow Mathematical Journal, vol. 63, no. 2, pp. 297-306Contributions to Journals: ArticlesTopological complexity of symplectic manifolds
Grant, M., Mescher, S.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/bitstream/2164/12620/1/Arxiv_Preprint.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/12620/2/Grant_Mescher_MZ_TopologicalComplexityOf_VoR.pdf
- [ONLINE] View publication in Mendeley
- [ONLINE] View publication in Scopus
Equivariant dimensions of groups with operators
Grant, M., Meir, E., Patchkoria, I.Working Papers: Working PapersDirected topological complexity of spheres
Borat, A., Grant, M.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/bitstream/2164/12627/1/1810.00339v1.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/12627/2/Borat_etal_JACT_Directed_Topological_Complexity_VOR.pdf
- [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
Crowley, D. J., Grant, M.Annals of K-Theory, vol. 5, no. 3, pp. 605-620Contributions to Journals: ArticlesMorita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity
Angel, A., Colman, H., Grant, M., Oprea, J.Theory and Applications of Categories, vol. 35, no. 7, pp. 179-195Contributions to Journals: ArticlesHopf Invariants for sectional category with applications to topological robotics
González, J., Grant, M., Vandembroucq, L.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/bitstream/2164/14705/1/HopfSecat2019_04_02.pdf
- [ONLINE] View publication in Mendeley
Bredon cohomology and robot motion planning
Farber, M., Grant, M., Lupton, G., Oprea, J.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/bitstream/2164/14931/1/180516_Farber_v100.pdf
- [ONLINE] https://msp.org/publications/policies/
- [ONLINE] View publication in Scopus
Symmetrized topological complexity
Grant, M.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/bitstream/2164/11219/1/1703.07142v1.pdf
- [ONLINE] View publication in Scopus
- [ONLINE] View publication in Mendeley
An upper bound for topological complexity
Farber, M., Grant, M., Lupton, G., Oprea, J.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/bitstream/2164/13613/1/1807.03994.pdf
- [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
González, J., Grant, M., Vandembroucq, L.Chapters in Books, Reports and Conference Proceedings: Conference Proceedings- [ONLINE] https://arxiv.org/abs/1607.08858
- [ONLINE] DOI: https://doi.org/10.1090/conm/702/14109
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/8314/1/1607.08858v1
Preface: Contemporary Mathematics
Grant, M., Lupton, G., Vandembroucq, L.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
Grant, M. (ed.), Lupton, G. (ed.), Vandembroucq, L. (ed.)Vol. 702, American Mathematical Society. 176 pagesBooks and Reports: BooksTopological complexity of subgroups of Artin's braid groups
Grant, M., Recio-Mitter, D.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/bitstream/2164/10481/1/1607.04830.pdf
Realizing homology classes up to cobordism
Grant, M., Szűcs, A., Terpai, T.Osaka Journal of Mathematics, vol. 54, no. 4, pp. 801-805Contributions to Journals: ArticlesThe Poincaré-Hopf Theorem for line fields revisited
Crowley, D., Grant, M.Journal of Geometry and Physics, vol. 117, pp. 187-196Contributions to Journals: Articles- [ONLINE] https://arxiv.org/abs/1612.04073
- [ONLINE] DOI: https://doi.org/10.1016/j.geomphys.2017.03.011
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/10265/1/1612.04073.pdf
New lower bounds for the topological complexity of aspherical spaces
Grant, M., Lupton, G., Oprea, J.Topology and its Applications, vol. 189, pp. 78-91Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1016/j.topol.2015.04.005
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/6192/1/1309.4192v1
A mapping theorem for topological complexity
Grant, M., Lupton, G., Oprea, J.Algebraic & Geometric Topology, vol. 15, no. 3, pp. 1643-1666Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.2140/agt.2015.15.1643
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/4668/1/agt_v15_n3_p10_p.pdf
Homologies are infinitely complex
Szucs, A., Grant, M.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
Gonzalez, J., Grant, M.Proceedings of the American Mathematical Society, vol. 143, no. 10, pp. 4503-4512Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1090/proc/12443
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/4739/1/1309.4346v2
On Self-Intersection Invariants
Grant, M.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
Gonzalez, J., Grant, M., Torres-Giese, E., Xicotencatl, M.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
Grant, M., Szucs, A.Bulletin of the London Mathematical Society, vol. 45, no. 2, pp. 329-340Contributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1112/blms/bds090
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/4145/1/1111.0249.pdf
Equivariant topological complexity
Colman, H., Grant, M.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
Grant, M., Lupton, G., Oprea, J.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
Eccles, P. J., Grant, M.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
Grant, M.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
Farber, M., Grant, M.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
Grant, M.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/bitstream/2164/4160/1/0709.2287v2.pdf
Robot motion planning, weights of cohomology classes, and cohomology operations
Farber, M., Grant, M.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
Eccles, P. J., Grant, M.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
Farber, M., Grant, M.Chapters in Books, Reports and Conference Proceedings: Conference ProceedingsTopological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles
Farber, M., Grant, M., Yuzvinsky, S.Chapters in Books, Reports and Conference Proceedings: Conference ProceedingsBordism Classes Represented by Multiple Point Manifolds of Immersed Manifolds
Eccles, P. J., Grant, M.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
