Fugly.

Contact information:

RLM 10.132,
  d.mccoy at math.utexas.edu


Duncan McCoy

I am a Bing Postdoctoral Fellow at UT Austin. This semester (Spring 2017) I am teaching '361: Theory of functions in a complex variable'. The course page is here

My research interests lie in low-dimensional topology, where I have been using surgery obstructions arising from the theory of 4-manifolds and Heegaard Floer homology to answer questions about knot theory and 3-manifolds. This has been particularly fruitful when applied to the branched double covers of alternating knots.

I completed my PhD at the University of Glasgow in 2016 under the supervision of Brendan Owens. My thesis is available from the arXiv and the University of Glasgow's repository.

I was an undergraduate at Caius College, Cambridge, where I also completed Part III. Under the supervision of Jacob Rasmussen, I wrote my Part III Essay on Josh Greene's "Lattices, Graphs, and Conway Mutation" paper.


Papers and preprints:

  1. Non-integer characterizing slopes for torus knots - arXiv
  2. On L-space knots obtained from unknotting arcs in alternating diagrams
    - with A. Donald & F. Vafaee - arXiv
  3. On 2-bridge knots with differing smooth and topological slice genera
    - with P. Feller
    - Proc. Amer. Math. Soc. 144 (2016), no. 12, 5435–5442. - arXiv
  4. On calculating the slice genera of 11- and 12-crossing knots
    - with L. Lewark - arXiv
  5. Bounds on alternating surgery slopes
    - Accepted Algebr. Geom. Topol. - arXiv
  6. Surgeries, sharp 4-manifolds and the Alexander polynomial - arXiv
  7. Non-integer surgery and branched double covers of alternating knots
    - J. Lond. Math. Soc. (2) 92 (2015), no. 2, 311–337 - arXiv
  8. Alternating knots with unknotting number one
    - Adv. Math. 305 (2017), 757–802 - arXiv

Talks

Talks that I have given, or will give, include:
2017
  • "Characterizing slopes for torus knots"
    - LA Joint Topology seminar, Caltech, 17th April
  • "Alternating surgeries"
    - Université du Québec à Montréal, CIRGET seminar, 10th March
  • "Characterizing slopes for torus knots" (video)
    - Isaac Newton Institute, 3-manifold workshop, 2nd February
2016
  • "Characterizing slopes for torus knots"
    - University of Glasgow, G&T seminar, 26th November
  • "Characterizing slopes for torus knots"
    - Hausdorff Institute, Seminar on knot concordance and 4-manifolds, 7th November
  • "Surgery and tangle replacement in alternating diagrams"
    - Rice University, Topology seminar, 26th September
  • "Surgery and tangle replacement in alternating diagrams"
    - UT Austin, Topology seminar, 12th September
  • "Surgery and tangle replacement in alternating diagrams"
    - Princeton University, Topology seminar, 24th March
2015
  • "The smooth and topological slice genera of two-bridge knots"
    - University of Glasgow, G&T seminar, 16th November
  • "Alternating knots with unknotting number one"
    - Université de Genève, Séminaire de Topologie et Géométrie, 5th November
  • "Alternating knots with unknotting number one"
    - 11th William Rowan Hamilton G&T Workshop, Trinity College, Dublin, 25th-29th August
  • "Surgeries on torus knots"
    - ECSTATIC Conference, Imperial College, 11-12th June
  • "Alternating knots with unknotting number one"
    - UT Austin, Topology seminar, 20th April
  • "Alternating knots with unknotting number one"
    - UCLA, Topology seminar, 17th April
  • "Alternating knots with unknotting number one"
    - Caltech, Topology seminar, 15th April
  • "Alternating knots with unknotting number one"
    - Michigan State University, G&T seminar, 31st March
  • "Surgeries and the Alexander polynomial"
    - University of Glasgow, G&T seminar, 2nd February
2014
  • "Surgery and tangle replacement in alternating diagrams"
    - Scottish Topology Seminar, Aberdeen, 28th November
  • "Alternating knots with unknotting number one"
    - University of Cambridge, DG&T seminar, 19th November
  • "Alternating knots with unknotting number one"
    - University of Oxford, Topology seminar, 9th June
  • "The Montesinos trick"
    - Young Topology Meeting UK, Imperial College, 6th June
  • "Alternating knots with unknotting number one"
    - Imperial College London, Junior Topology seminar, 5th June
  • "Alternating knots with unknotting number one"
    - University of Glasgow, G&T seminar, 20th January

Working Group

In the Winter of 2015 I co-organised a working group with Haris Stylianakis on the topology and geometry of 3-manifolds.