Dr Mark Grant

Dr Mark Grant
MA (Edin), PhD (Manc)

Senior Lecturer

Overview
Dr Mark Grant
Dr Mark Grant

Contact Details

Telephone
work +44 (0)1224 273391
Email
Address
The University of Aberdeen Fraser Noble Building FN137
Web Links

http://homepages.abdn.ac.uk/mark.grant/pages/

Research

Research Interests

Dr Grant is interested in Algebraic and Differential Topology and their applications, particularly to Robotics.

Teaching

Teaching Responsibilities

 
  • SX3007 Mathematical Foundations of Everyday Life (First Half-Session 2019/20)
  • SMSTC Algebraic Topology (Graduate course) (First Half-Session 2019/20)
  • EG1504 Engineering Mathematics 1 (Second Half-Session 2019/20)
  • MX4549 Geometry (Second Half-Session 2019/20)
Publications

Publications 

Currently viewing:

Page 1 of 1 Results 1 to 33 of 33

  • Borat, A & Grant, M 2020, 'Directed topological complexity of spheres', Journal of applied and computational topology, vol. 4, pp. 3-9. [Online] DOI: https://doi.org/10.1007/s41468-019-00033-y
  • Grant, M, Meir, E & Patchkoria, I 2020 'Equivariant dimensions of groups with operators' ArXiv. <> [Online] DOI: https://arxiv.org/pdf/1912.01692.pdf
  • Grant, M & Sienicka, A 2020, 'Isotopy and homeomorphism of closed surface braids', Glasgow Mathematical Journal. [Online] DOI: https://doi.org/10.1017/S0017089520000208
  • Angel, A, Colman, H, Grant, M & Oprea, J 2020, 'Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity', Theory and Applications of Categories, vol. 35, no. 7, pp. 179-195. <> [Online] DOI: https://arxiv.org/abs/1908.04949v4
  • Crowley, DJ & Grant, M 2020, 'The Topological Period-Index Conjecture for spinc 6-manifolds', Annals of K-Theory. <> [Online] DOI: https://arxiv.org/abs/1802.01296
  • Grant, M & Mescher, S 2020, 'Topological complexity of symplectic manifolds', Mathematische Zeitschrift, vol. 295, pp. 667–679. [Online] DOI: https://doi.org/10.1007/s00209-019-02366-x
  • Farber, M, Grant, M, Lupton, G & Oprea, J 2019, 'An upper bound for topological complexity', Topology and its Applications, vol. 255, pp. 109-125. [Online] DOI: https://doi.org/10.1016/j.topol.2019.01.007
  • Farber, M, Grant, M, Lupton, G & Oprea, J 2019, 'Bredon cohomology and robot motion planning', Algebraic & Geometric Topology, vol. 19, no. 4, pp. 2023-2059. [Online] DOI: https://doi.org/10.2140/agt.2019.19.2023
  • González, J, Grant, M & Vandembroucq, L 2019, 'Hopf Invariants for sectional category with applications to topological robotics', Quarterly Journal of Mathematics, vol. 70, no. 4, pp. 1209-1252. [Online] DOI: https://doi.org/10.1093/qmath/haz019
  • Grant, M 2019, 'Symmetrized topological complexity', Journal of Topology and Analysis, vol. 11, no. 2, pp. 387-403. [Online] DOI: https://doi.org/10.1142/S1793525319500183
  • González, J, Grant, M & Vandembroucq, L 2018, Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes. in M Grant, G Lupton & L Vandembroucq (eds), Topological complexity and related topics. vol. 702, Contemporary Mathematics, American Mathematical Society, pp. 133-150. [Online] DOI: https://doi.org/10.1090/conm/702/14109
  • Grant, M, Lupton, G & Vandembroucq, L (eds) 2018, Topological Complexity and Related Topics: Mini-Workshop Topological Complexity and Related Topics February 28–March 5, 2016 Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany. Contemporary Mathematics, vol. 702, vol. 702, American Mathematical Society.
  • Grant, M & Recio-Mitter, D 2018, Topological complexity of subgroups of Artin's braid groups. in M Grant, G Lupton & L Vandembroucq (eds), Topological complexity and related topics. vol. 702, Contemporary Mathematics, American Mathematical Society. [Online] DOI: https://doi.org/10.1090/conm/702/14105
  • Grant, M, Szűcs, A & Terpai, T 2017, 'Realizing homology classes up to cobordism', Osaka Journal of Mathematics, vol. 54, no. 4, pp. 801-805. <> [Online] DOI: https://arxiv.org/abs/1602.05759
  • Crowley, D & Grant, M 2017, 'The Poincaré-Hopf Theorem for line fields revisited', Journal of Geometry and Physics, vol. 117, pp. 187-196. [Online] DOI: https://doi.org/10.1016/j.geomphys.2017.03.011
  • Grant, M, Lupton, G & Oprea, J 2015, 'A mapping theorem for topological complexity', Algebraic & Geometric Topology, vol. 15, no. 3, pp. 1643-1666. [Online] DOI: https://doi.org/10.2140/agt.2015.15.1643
  • Szucs, A & Grant, M 2015, 'Homologies are infinitely complex', Topological Methods in Nonlinear Analysis, vol. 45, no. 1, pp. 55-62. [Online] DOI: https://doi.org/10.12775/TMNA.2015.003
  • Grant, M, Lupton, G & Oprea, J 2015, 'New lower bounds for the topological complexity of aspherical spaces', Topology and its Applications, vol. 189, pp. 78-91. [Online] DOI: https://doi.org/10.1016/j.topol.2015.04.005
  • Gonzalez, J & Grant, M 2015, 'Sequential motion planning of non-colliding particles in Euclidean spaces', Proceedings of the American Mathematical Society, vol. 143, no. 10, pp. 4503-4512. [Online] DOI: https://doi.org/10.1090/proc/12443
  • Colman, H & Grant, M 2013, 'Equivariant topological complexity', Algebraic & Geometric Topology, vol. 12, no. 4, pp. 2299-2316. [Online] DOI: https://doi.org/10.2140/agt.2012.12.2299
  • Grant, M 2013, 'On Self-Intersection Invariants', Glasgow Mathematical Journal, vol. 55, no. 2, pp. 259-273. [Online] DOI: https://doi.org/10.1017/S0017089512000481
  • Grant, M & Szucs, A 2013, 'On realizing homology classes by maps of restricted complexity', Bulletin of the London Mathematical Society, vol. 45, no. 2, pp. 329-340. [Online] DOI: https://doi.org/10.1112/blms/bds090
  • Grant, M, Lupton, G & Oprea, J 2013, 'Spaces of topological complexity one', Homology, Homotopy and Applications, vol. 15, no. 2, pp. 73-81. [Online] DOI: https://doi.org/10.4310/HHA.2013.v15.n2.a4
  • Gonzalez, J, Grant, M, Torres-Giese, E & Xicotencatl, M 2013, 'Topological complexity of motion planning in projective product spaces', Algebraic & Geometric Topology, vol. 13, no. 2, pp. 1027-1047. [Online] DOI: https://doi.org/10.2140/agt.2013.13.1027
  • Eccles, PJ & Grant, M 2012, 'Self-intersections of immersions and Steenrod operations', Acta Mathematica Hungarica, vol. 137, no. 4, pp. 272-281. [Online] DOI: https://doi.org/10.1007/s10474-011-0189-9
  • Grant, M 2012, 'Topological complexity, fibrations and symmetry', Topology and its Applications, vol. 159, no. 1, pp. 88-97. [Online] DOI: https://doi.org/10.1016/j.topol.2011.07.025
  • Farber, M & Grant, M 2009, 'Topological Complexity of Configuration Spaces', Proceedings of the American Mathematical Society, vol. 137, no. 5, pp. 1841-1847. [Online] DOI: https://doi.org/10.1090/S0002-9939-08-09808-0
  • Grant, M 2009, 'Topological complexity of motion planning and Massey products', Banach Center Publications, vol. 85, pp. 193-203. [Online] DOI: https://doi.org/10.4064/bc85-0-14
  • Farber, M & Grant, M 2008, 'Robot motion planning, weights of cohomology classes, and cohomology operations', Proceedings of the American Mathematical Society, vol. 136, no. 9, pp. 3339-3349. [Online] DOI: https://doi.org/10.1090/S0002-9939-08-09529-4#sthash.ulDhWxF6.dpuf
  • Eccles, PJ & Grant, M 2007, 'Bordism groups of immersions and classes represented by self-intersections', Algebraic & Geometric Topology, vol. 7, pp. 1081-1097. [Online] DOI: https://doi.org/10.2140/agt.2007.7.1081
  • Farber, M & Grant, M 2007, Symmetric Motion Planning. in M Farber, R Ghrist, M Burger & D Koditschek (eds), Topology and Robotics. Contemporary Mathematics Series, vol. 438, American Mathematical Society, Providence, pp. 85-104, Workshop on Topology and Robotics, Switzerland, 10/07/06.
  • Farber, M, Grant, M & Yuzvinsky, S 2007, Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles. in M Farber, R Ghrist, M Burger & D Koditschek (eds), Topology and Robotics. Contemporary Mathematics, vol. 438, American Mathematical Society, Providence, pp. 75-83, Workshop on Topology and Robotics, Switzerland, 10/07/06.
  • Eccles, PJ & Grant, M 2006, 'Bordism Classes Represented by Multiple Point Manifolds of Immersed Manifolds', Proceedings of the Steklov Institute of Mathematics, vol. 252, no. 1, pp. 47-52. [Online] DOI: https://doi.org/10.1134/S0081543806010068
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