Next year I will be taking up a position at Université du Québec à Montréal. This webpage is no longer maintained.

I am a Bing Postdoctoral Fellow at the University of Texas at Austin. My research interests lie in low-dimensional topology, where I have been using techniques arising from the theory of 4-manifolds and Heegaard Floer homology to study knots and 3-manifolds. I have a particular interest in Dehn surgery problems and classical knot invariants.

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. Smoothly embedding Seifert fibered spaces in S^4
   - with A. Issa - arXiv
2. The realization problem for non-integer Seifert fibered surgeries
   - with A. Issa - arXiv
3. On the characterising slopes of hyperbolic knots
   - Accepted Math. Res. Let. - arXiv
4. On Seifert fibered spaces bounding definite manifolds
   - with A. Issa - arXiv
5. Non-integer characterizing slopes for torus knots
   - Accepted Comm. Anal. Geom. - arXiv
6. On L-space knots obtained from unknotting arcs in alternating diagrams
   - with A. Donald & F. Vafaee - arXiv
   - New York J. Math. 25 (2019), 518–540.
7. On 2-bridge knots with differing smooth and topological slice genera
   - with P. Feller - arXiv
   - Proc. Amer. Math. Soc. 144 (2016), no. 12, 5435–5442.
8. On calculating the slice genera of 11- and 12-crossing knots
   - with L. Lewark - arXiv
   - Exp. Math. 28 (2019), no. 1, 81–94.
9. Bounds on alternating surgery slopes - arXiv
   - Algebr. Geom. Topol. 17 (2017), no. 5, 2603–2634.
10. Surgeries, sharp 4-manifolds and the Alexander polynomial - arXiv
11. Non-integer surgery and branched double covers of alternating knots
    - J. Lond. Math. Soc. (2) 92 (2015), no. 2, 311–337. - arXiv
12. Alternating knots with unknotting number one
    - Adv. Math. 305 (2017), 757–802. - arXiv

Talks

• "Characterizing slopes for hyperbolic and torus knots"
  - Oklahoma State University, Topology Seminar, 4th December
• "Characterizing slopes for hyperbolic and torus knots"
  - Temple University, PATCH Seminar, 28th September
• "Characterizing slopes for hyperbolic and torus knots"
  - UT Austin, Topology Seminar, 24th September
• "Lattices, embeddings and Seifert fibered spaces"
  - Princeton University, Low-dimensional topology RTG mini-conference, 22nd-24th June
• "Lattices, embeddings and Seifert fibered spaces"
  - Boston College, Topology Seminar, 22nd March

• "Non-integer Seifert fibered surgeries"
  - Columbia University, SGGTC Seminar, 29th September
• "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

• "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

• "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

• "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