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Institute of Mathematics, Fraser Noble Building, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
Tel: +44 (0)1224 27 3391 Fax: +44 (0)1224 27 2607 Email: mark.grant(at)abdn.ac.uk
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Institute of Mathematics, Fraser Noble Building, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
Tel: +44 (0)1224 27 3391 Fax: +44 (0)1224 27 2607 Email: mark.grant(at)abdn.ac.uk
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I am a reader in the Institute of Mathematics at the University of Aberdeen, with interests in algebraic and differential topology and their applications. You can find out more about my research interests by browsing my publications below. Here are links to my Google Scholar, MathSciNet and MathOverflow profiles.
I am on the editorial boards of the journals Proceedings of the Royal Society of Edinburgh Section A: Mathematics and Topological Methods in Nonlinear Analysis.
My CV as of February 2024.
EG1011 Introductory Mathematics (First Half-Session 2023/24)
MX4549 Geometry (Second Half-Session 2023/24)
All teaching materials will be made available via MyAberdeen.
Baylee Schutte (2021—)
David Recio-Mitter (2015—2018)
Projective span of Wall manifolds (with Baylee Schutte), to appear in Bol. Soc. Mat. Méx.
Comparison of equivariant cohomological dimensions (with Kevin Li, Ehud Meir and Irakli Patchkoria), to appear in Israel J. Math..
Parametrised topological complexity of group epimorphisms, Topol. Methods Nonlinear Anal. 60(1) (2022), 287—303.
Equivariant dimensions of groups with operators (with Ehud Meir and Irakli Patchkoria), Groups Geom. Dyn. 16(3) (2022), 1049—1075.
Isotopy and homeomorphism of closed surface braids (with Agata Sienicka), Glasgow Math. J. 63(2) (2021), 297—306. Published online.
The Topological Period-Index Conjecture for spinc 6-manifolds (with Diarmuid Crowley), Ann. K-Theory, 5-3 (2020), 605—620. Published online.
Topological complexity of symplectic manifolds (with Stephan Mescher), Math Z. 295 (2020), 667—679. Published online.
Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity (with Andrés Ángel, Hellen Colman and John Oprea), Theory Appl. Categ. 35 (2020), 179—195. Published online.
Directed topological complexity of spheres (with Ayşe Borat), J. Appl. Comput. Topol. 4 (2020), 3—9. Published online.
Hopf Invariants for sectional category with applications to topological robotics (with Jesús González and Lucile Vandembroucq), Q. J. Math. 70 (2019), no.4, 1209—1252. Published online.
Bredon cohomology and robot motion planning (with Michael Farber, Gregory Lupton and John Oprea), Algebr. Geom. Topol. 19 (2019), 2023—2059.
Symmetrized topological complexity, J. Topol. Anal. 11 (2019), no. 2, 387—403.
An upper bound for topological complexity (with Michael Farber, Gregory Lupton and John Oprea), Topology Appl. 255 (2019), 109—125.
Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes (with Jesús González and Lucile Vandembroucq), in “Topological Complexity and Related Topics”, M. Grant, G. Lupton and L. Vandembroucq (eds), Contemp. Math. 702 (2018), 133—150.
Topological complexity of subgroups of Artin's braid groups (with David Recio-Mitter), in “Topological Complexity and Related Topics”, M. Grant, G. Lupton and L. Vandembroucq (eds), Contemp. Math. 702 (2018), 165—176.
Realizing homology classes up to cobordism (with András Szűcs and Tamás Terpai), Osaka J. Math. 54 (2017), no. 4, 803—807. Published online.
The Poincaré-Hopf Theorem for line fields revisited (with Diarmuid Crowley), J. Geom. Phys. 117 (2017), 187—196. Published online.
A mapping theorem for topological complexity (with Gregory Lupton and John Oprea), Algebr. Geom. Topol. 15 (2015), 1643—1666.
Sequential motion planning of non-colliding particles in Euclidean spaces (with Jesús González), Proc. Amer. Math. Soc. 143 (2015), 4503—4512.
New lower bounds for the topological complexity of aspherical spaces (with Gregory Lupton and John Oprea), Topology Appl. 189 (2015), 78—91. Published online.
Homologies are infinitely complex (with András Szűcs), Topol. Methods Nonlinear Anal. 45 (2015), No. 1, 55—61.
Spaces of Topological Complexity One (with Gregory Lupton and John Oprea), Homology Homotopy Appl. 15 (2013), No. 2, 73—81.
On realizing homology classes by maps of restricted complexity (with András Szűcs), Bull. London Math. Soc. 45 (2013), 329—340.
Topological complexity of motion planning in projective product spaces (with Jesús González, Enrique Torres-Giese and Miguel Xicoténcatl), Algebr. Geom. Topol. 13 (2013), 1027—1047.
On self-intersection invariants, Glasgow Math. J. 55 (2013), 259—273.
Equivariant topological complexity (with Hellen Colman), Algebr. Geom. Topol. 12 (2012), 2299—2316.
Self-intersections of Immersions and Steenrod Operations (with Peter J. Eccles), Acta Math. Hungar. 137 (2012), 272—281.
Topological complexity, fibrations and symmetry, Topology Appl. 159 (2012), 88—97.
Topological complexity of configuration spaces (with Michael Farber), Proc. Amer. Math. Soc. 137 (2009), 1841—1847.
Topological complexity of motion planning and Massey products, In “Algebraic Topology – Old and New: M. M. Postnikov Memorial Conference”, M Golasiński et al (eds), Banach Center Publ. 85 (2009), 193—203.
Robot motion planning, weights of cohomology classes, and cohomology operations (with Michael Farber), Proc. Amer. Math. Soc. 136 (2008), 3339—3349.
Symmetric Motion Planning (with Michael Farber), In “Topology and Robotics”, M Farber, R Ghrist, M Burger and D Koditschek (eds), Contemp. Math. 438 (2007), 85—104.
Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles (with Michael Farber and Sergey Yuzvinsky), In “Topology and Robotics”, M Farber, R Ghrist, M Burger and D Koditschek (eds), Contemp. Math. 438 (2007), 75—83.
Bordism Groups of Immersions and Classes Represented by Self-intersections (with Peter J. Eccles), Algebr. Geom. Topol. 7 (2007), 1081—1097.
Bordism classes represented by multiple point manifolds of immersed manifolds (with Peter J. Eccles), Proc. Steklov Inst. Math. 252 (2006), 47—52.
Bordism of Immersions, Thesis, University of Manchester, 2006.
Outside In on YouTube
The Optiverse on YouTube
The de Neve/Hills sphere eversion on YouTube and an interactive model
MathSciNet Search (subscription required)
MathOverflow (a question and answer site for research level Mathematics)
arXiv.org: Mathematical e-prints
