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 lowdimensional topology, where I have been using surgery obstructions
arising from the theory of 4manifolds and Heegaard Floer homology to answer questions about knot theory
and 3manifolds. 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:

Noninteger characterizing slopes for torus knots
 arXiv

On Lspace knots obtained from unknotting arcs in alternating diagrams
 with A. Donald & F. Vafaee
 arXiv

On 2bridge knots with differing smooth and topological slice genera
 with P. Feller
 Proc. Amer. Math. Soc. 144 (2016), no. 12, 5435–5442.
 arXiv

On calculating the slice genera of 11 and 12crossing knots
 with L. Lewark  arXiv

Bounds on alternating surgery slopes
 Accepted Algebr. Geom. Topol.
 arXiv

Surgeries, sharp 4manifolds and the Alexander polynomial
 arXiv

Noninteger surgery and branched double covers of alternating knots
 J. Lond. Math. Soc. (2) 92 (2015), no. 2, 311–337
 arXiv

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, 3manifold 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 4manifolds, 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 twobridge 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, 25th29th August

"Surgeries on torus knots"
 ECSTATIC Conference,
Imperial College, 1112th 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 coorganised a working group with Haris Stylianakis on the
topology and geometry of 3manifolds.
