Institute of Mathematics,
Fraser Noble Building,
University of Aberdeen,
Aberdeen AB24 3UE,
Tel: +44 (0)1224 27 3391
Fax: +44 (0)1224 27 2607
I am a senior lecturer 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 and MathSciNet profiles.
David Recio-Mitter is my former PhD student.
I am 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 2020.
SMSTC Topology (First Half-Session 2019/20)
MX4549 Geometry (Second Half-Session 2019/20
EG1504 Engineering Mathematics 1 (Second Half-Session 2019/20)
All teaching materials (except for the SMSTC course) will be made available via MyAberdeen.
Isotopy and homeomorphism of closed surface braids (with Agata Sienicka), to appear in Glasgow Math. J. Published online.
The Topological Period-Index Conjecture for spinc 6-manifolds (with Diarmuid Crowley), to appear in Ann. K-Theory.
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.
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.
Symmetrized topological complexity, J. Topol. Anal. 11 (2019), no. 2, 387—403.
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.
The Poincaré-Hopf Theorem for line fields revisited (with Diarmuid Crowley), J. Geom. Phys. 117 (2017), 187—196. Published online.
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.
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.
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 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.
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.
“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 175th 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)
Outside In on YouTube
The Optiverse on YouTube
MathSciNet Search (subscription required)
MathOverflow (a question and answer site for research level Mathematics)
arXiv.org: Mathematical e-prints