Dr Mark Grant | People | The University of Aberdeen

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

Personal Website

Google Scholar

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

Courses

Publications

Page 1 of 1 Results 1 to 41 of 41

Projective Span of Wall Manifolds
2024 - Published
Grant, M., Schutte, B.
Boletin Sociedad Matematica Mexicana, vol. 30, 75
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1007/s40590-024-00648-x
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/24450/1/Grant_etal_BSMM_Projective_Span_Of_AAM.pdf
Equivariant topological complexities
2024 - Accepted/In press
Grant, M.
Topology and AI. European Mathematical Society Publishing House
Chapters in Books, Reports and Conference Proceedings: Chapters (Peer-Reviewed)
Equivariant topological complexities
2024 - Published
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
2023 - Accepted/In press
Grant, M., Li, K., Meir Ben Efraim, E., Patchkoria, I.
Israel Journal of Mathematics
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2302.08574
Comparison of equivariant cohomological dimensions
2023 - Published
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
2022 - Published
Grant, M., Meir, E., Patchkoria, I.
Groups, Geometry and Dynamics, vol. 16, no. 3
Contributions 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
2022 - Published
Grant, M.
Topological Methods in Nonlinear Analysis, vol. 60, no. 1, pp. 287-303
Contributions to Journals: Articles
- [ONLINE] http://arxiv.org/abs/2106.02667v1
- [ONLINE] DOI: https://doi.org/10.12775/TMNA.2021.056
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/16786/1/2106.02667v1.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/16786/2/Grant_TPNA_Parametrised_Topological_Complexity_AAM.pdf
Isotopy and homeomorphism of closed surface braids
2021 - Published
Grant, M., Sienicka, A.
Glasgow Mathematical Journal, vol. 63, no. 2, pp. 297-306
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1017/S0017089520000208
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/15364/1/Grant_Sienicka_GMJ_IsotopyAndHomeomorphism_AAM.pdf
- [ONLINE] View publication in Scopus
Topological complexity of symplectic manifolds
2020 - Published
Grant, M., Mescher, S.
Mathematische Zeitschrift, vol. 295, pp. 667–679
Contributions 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
2020 - Published
Grant, M., Meir, E., Patchkoria, I.
Working Papers: Working Papers
- [ONLINE] https://arxiv.org/abs/1912.01692v3
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/15945/1/Grant_etal_Arxiv_Equivariant_Dimensions_Groups.pdf
Directed topological complexity of spheres
2020 - Published
Borat, A., Grant, M.
Journal of applied and computational topology, vol. 4, pp. 3-9
Contributions 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 spin^c 6-manifolds
2020 - Published
Crowley, D. J., Grant, M.
Annals of K-Theory, vol. 5, no. 3, pp. 605-620
Contributions to Journals: Articles
- [ONLINE] https://arxiv.org/abs/1802.01296
- [ONLINE] DOI: https://doi.org/10.2140/akt.2020.5.605
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/15045/1/Grant_etal_akt_Topological_VOR.pdf
Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity
2020 - Published
Angel, A., Colman, H., Grant, M., Oprea, J.
Theory and Applications of Categories, vol. 35, no. 7, pp. 179-195
Contributions to Journals: Articles
- [ONLINE] http://www.tac.mta.ca/tac/volumes/35/7/35-07.pdf
- [ONLINE] View publication in Scopus
Hopf Invariants for sectional category with applications to topological robotics
2019 - Published
González, J., Grant, M., Vandembroucq, L.
Quarterly Journal of Mathematics, vol. 70, no. 4, pp. 1209-1252
Contributions 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
2019 - Published
Farber, M., Grant, M., Lupton, G., Oprea, J.
Algebraic & Geometric Topology, vol. 19, no. 4, pp. 2023-2059
Contributions 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
2019 - Published
Grant, M.
Journal of Topology and Analysis, vol. 11, no. 2, pp. 387-403
Contributions 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
2019 - Published
Farber, M., Grant, M., Lupton, G., Oprea, J.
Topology and its Applications, vol. 255, pp. 109-125
Contributions 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
2018 - Published
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
2018 - Published
Grant, M., Lupton, G., Vandembroucq, L.
Contemporary Mathematics, vol. 702, pp. v-vii
Contributions 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
2018 - Published
Grant, M. (ed.), Lupton, G. (ed.), Vandembroucq, L. (ed.)
Vol. 702, American Mathematical Society. 176 pages
Books and Reports: Books
Topological complexity of subgroups of Artin's braid groups
2018 - Published
Grant, M., Recio-Mitter, D.
Topological complexity and related topics. Grant, M., Lupton, G., Vandembroucq, L. (eds.). American Mathematical Society
Chapters 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
2017 - Published
Grant, M., Szűcs, A., Terpai, T.
Osaka Journal of Mathematics, vol. 54, no. 4, pp. 801-805
Contributions to Journals: Articles
- [ONLINE] https://projecteuclid.org/euclid.ojm/1508486581
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/7968/1/1602.05759v1
The Poincaré-Hopf Theorem for line fields revisited
2017 - Published
Crowley, D., Grant, M.
Journal of Geometry and Physics, vol. 117, pp. 187-196
Contributions 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
2015 - Published
Grant, M., Lupton, G., Oprea, J.
Topology and its Applications, vol. 189, pp. 78-91
Contributions 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
2015 - Published
Grant, M., Lupton, G., Oprea, J.
Algebraic & Geometric Topology, vol. 15, no. 3, pp. 1643-1666
Contributions 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
2015 - Published
Szucs, A., Grant, M.
Topological Methods in Nonlinear Analysis, vol. 45, no. 1, pp. 55-62
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.12775/TMNA.2015.003
Sequential motion planning of non-colliding particles in Euclidean spaces
2015 - Published
Gonzalez, J., Grant, M.
Proceedings of the American Mathematical Society, vol. 143, no. 10, pp. 4503-4512
Contributions 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
2013 - Published
Grant, M.
Glasgow Mathematical Journal, vol. 55, no. 2, pp. 259-273
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1017/S0017089512000481
Topological complexity of motion planning in projective product spaces
2013 - Published
Gonzalez, J., Grant, M., Torres-Giese, E., Xicotencatl, M.
Algebraic & Geometric Topology, vol. 13, no. 2, pp. 1027-1047
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.2140/agt.2013.13.1027
On realizing homology classes by maps of restricted complexity
2013 - Published
Grant, M., Szucs, A.
Bulletin of the London Mathematical Society, vol. 45, no. 2, pp. 329-340
Contributions 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
2013 - Published
Colman, H., Grant, M.
Algebraic & Geometric Topology, vol. 12, no. 4, pp. 2299-2316
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.2140/agt.2012.12.2299
Spaces of topological complexity one
2013 - Published
Grant, M., Lupton, G., Oprea, J.
Homology, Homotopy and Applications, vol. 15, no. 2, pp. 73-81
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.4310/HHA.2013.v15.n2.a4
Self-intersections of immersions and Steenrod operations
2012 - Published
Eccles, P. J., Grant, M.
Acta Mathematica Hungarica, vol. 137, no. 4, pp. 272-281
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1007/s10474-011-0189-9
Topological complexity, fibrations and symmetry
2012 - Published
Grant, M.
Topology and its Applications, vol. 159, no. 1, pp. 88-97
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.topol.2011.07.025
Topological Complexity of Configuration Spaces
2009 - Published
Farber, M., Grant, M.
Proceedings of the American Mathematical Society, vol. 137, no. 5, pp. 1841-1847
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1090/S0002-9939-08-09808-0
Topological complexity of motion planning and Massey products
2009 - Published
Grant, M.
Banach Center Publications, vol. 85, pp. 193-203
Contributions 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
2008 - Published
Farber, M., Grant, M.
Proceedings of the American Mathematical Society, vol. 136, no. 9, pp. 3339-3349
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1090/S0002-9939-08-09529-4#sthash.ulDhWxF6.dpuf
Bordism groups of immersions and classes represented by self-intersections
2007 - Published
Eccles, P. J., Grant, M.
Algebraic & Geometric Topology, vol. 7, pp. 1081-1097
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.2140/agt.2007.7.1081
Symmetric Motion Planning
2007 - Published
Farber, M., Grant, M.
Chapters in Books, Reports and Conference Proceedings: Conference Proceedings
Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles
2007 - Published
Farber, M., Grant, M., Yuzvinsky, S.
Chapters in Books, Reports and Conference Proceedings: Conference Proceedings
Bordism Classes Represented by Multiple Point Manifolds of Immersed Manifolds
2006 - Published
Eccles, P. J., Grant, M.
Proceedings of the Steklov Institute of Mathematics, vol. 252, no. 1, pp. 47-52
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1134/S0081543806010068

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Books and Reports

Books (1)

Chapters in Books, Reports and Conference Proceedings

Chapters (Peer-Reviewed) (2)

Conference Proceedings (3)

Contributions to Journals

Articles (31)

Editorials (1)

Working Papers

Working Papers (1)

Preprint Papers (2)

Update

Biography

Research Overview

Courses

Projective Span of Wall Manifolds

Equivariant topological complexities

Equivariant topological complexities

Comparison of equivariant cohomological dimensions

Comparison of equivariant cohomological dimensions

Equivariant dimensions of groups with operators

Parametrised topological complexity of group epimorphisms

Isotopy and homeomorphism of closed surface braids

Topological complexity of symplectic manifolds

Equivariant dimensions of groups with operators

Directed topological complexity of spheres

The Topological Period-Index Conjecture for spinc 6-manifolds

Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity

Hopf Invariants for sectional category with applications to topological robotics

Bredon cohomology and robot motion planning

Symmetrized topological complexity

An upper bound for topological complexity

Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes

Preface: Contemporary Mathematics

Topological Complexity and Related Topics: Mini-Workshop Topological Complexity and Related Topics February 28–March 5, 2016 Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany

Topological complexity of subgroups of Artin's braid groups

Realizing homology classes up to cobordism

The Poincaré-Hopf Theorem for line fields revisited

New lower bounds for the topological complexity of aspherical spaces

A mapping theorem for topological complexity

Homologies are infinitely complex

Sequential motion planning of non-colliding particles in Euclidean spaces

On Self-Intersection Invariants

Topological complexity of motion planning in projective product spaces

On realizing homology classes by maps of restricted complexity

Equivariant topological complexity

Spaces of topological complexity one

Self-intersections of immersions and Steenrod operations

Topological complexity, fibrations and symmetry

Topological Complexity of Configuration Spaces

Topological complexity of motion planning and Massey products

Robot motion planning, weights of cohomology classes, and cohomology operations

Bordism groups of immersions and classes represented by self-intersections

Symmetric Motion Planning

Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles

Bordism Classes Represented by Multiple Point Manifolds of Immersed Manifolds

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Books and Reports

Chapters in Books, Reports and Conference Proceedings

Contributions to Journals

Working Papers

The Topological Period-Index Conjecture for spin^c 6-manifolds