Mark Grant's Homepage

About Me

I am a lecturer in the Institute of Pure and Applied 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 and MathSciNet profiles.

David Recio-Mitter is my PhD student.

I am organizer of the Aberdeen topology seminar, and one of the organizers of the Scottish Topology Seminar. If you would like to give a talk, please send me an email.

I am on the editorial board of the journal Proceedings of the Royal Society of Edinburgh Section A: Mathematics.

I am also a keen participant at MathOverflow, and have an Erdős number of 3.

My CV as of May 2018.

Teaching

• MA1006 Algebra (First Half-Session 2017/18)

• SX3007 Mathematical Foundations of Everyday Life (First Half-Session 2017/18)

• MX3036 Metric and Topological Spaces (First Half-Session 2017/18)

• SMSTC Topology (First Half-Session 2017/18)

All teaching materials (except for the SMSTC course) will be made available via MyAberdeen. My weekly timetable for the Autumn semester is here.

Research Papers

• An upper bound for topological complexity (with Michael Farber, Gregory Lupton and John Oprea), submitted.

• Topological complexity of symplectic manifolds (with Stephan Mescher), submitted.

• The Topological Period-Index Problem for spinc 6-manifolds (with Diarmuid Crowley), submitted.

• Bredon cohomology and robot motion planning (with Michael Farber, Gregory Lupton and John Oprea), submitted.

• Hopf Invariants for sectional category with applications to topological robotics (with Jesús González and Lucile Vandembroucq), submitted.

• Symmetrized topological complexity, to appear in J. Topol. Anal. Published online.

• 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.

Slideshows

• “Symmetrized topological complexity” - Delivered at Applied Topology in Będlewo (26/6/17)

• “The Poincaré-Hopf Theorem for line fields revisited” - Delivered at the University of Southampton topology seminar (30/1/2017)

• “Topology and robot motion planning” - Delivered to the University of Aberdeen Maths Club (18/11/15)

• “Lower bounds for the topological complexity of groups” - Delivered at the University of Leicester Pure Mathematics seminar (23/11/13)

• “On immersions in homology classes” - Delivered at the British Topology Meeting, Edinburgh (3/9/11)

• “Topological complexity of motion planning algorithms” - Survey talk at the School of Informatics, University of Edinburgh (31/3/11)

• “Self-intersections of immersions and Steenrod operations” - Delivered at the Edinburgh Topology seminar (23/11/07)

• “Turning spheres inside-out” - Public talk for alumni of Durham University at the 175^th anniversary celebrations (8/9/07)

• “Sectional category weight and topological complexity” - Delivered at the BMC2007, Swansea (17/4/07) and at the M. M. Postnikov Memorial Conference, Bedlewo, Poland (21/6/07)

Sphere eversions

• Outside In on YouTube

• The Optiverse on YouTube

• The de Neve/Hills sphere eversion on YouTube and an interactive model

• Download a fully interactive sphere eversion!

Useful links

• MathSciNet Search (subscription required)

• MathOverflow (a question and answer site for research level Mathematics)

• arXiv.org: Mathematical e-prints

• Algebraic Topology Discussion Group

• Transpennine Topology Triangle

• Bristol Rovers F.C.