University of Durham --- Department of Mathematical Sciences



Preprints under review

Almost positive links are strongly quasipositive, (with Peter Feller and Lukas Lewark).
A calculus for flow categories, (with Patrick Orson and Dirk Schuetz).
The Dold-Whitney theorem and the Sato-Levine invariant.
An sl(n) stable homotopy type for matched diagrams, (with Dan Jones and Dirk Schuetz).
On spectral sequences from Khovanov homology, (with Raphael Zentner).

Non-pure preprints under review

Social learning errors and the evolution of material culture, (with Lauren Scanlon, Jeremy Kendal, and Jamie Tehrani).


Published or accepted papers

On the functoriality of Khovanov-Floer theories, (with John Baldwin and Matt Hedden). To appear in Adv. Math.
Khovanov homotopy calculations using flow category calculus, (with Patrick Orson and Dirk Schuetz). To appear in Experiment. Math.
Upsilon-like concordance invariants from sl(n) knot cohomology, (with Lukas Lewark). To appear in Geom. Topol.
Framed cobordism and flow category moves, (with Patrick Orson and Dirk Schuetz). Algebr. Geom. Topol. 18 (2018), 2821-2858.
A Khovanov stable homotopy type for colored links, (with Patrick Orson and Dirk Schuetz), Algebr. Geom. Topol. 17 (2017) 1261–1281.
Morse moves in flow categories, (with Dan Jones and Dirk Schuetz), Indiana Univ. Math. J. 2017 66(5): 1603-1657.
New quantum obstructions to sliceness, (with Lukas Lewark) Proc. Lond. Math. Soc. 2016 112(1): 81-114.
2-strand twisting and knots with identical quantum knot homologies, Geom. Topol. 2014 18(2): 873-895.
The quantum sl(N) graph invariant and a moduli space, (with Raphael Zentner) Int. Math. Res. Not. IMRN 2014, Vol. 2014, No. 7: 1956-1972.
The Kanenobu knots and Khovanov-Rozansky homology, Proc. Amer. Math. Soc. 2014 142(4): 1447-1455.
A note on Gornik's perturbation of Khovanov-Rozansky homology, Algebr. Geom. Topol. 2012 12(1): 293-305.
Computable bounds for Rasmussen's concordance invariant, Compos. Math. 2011 147(2): 661-668.
Casson-type moduli spaces for definite 4-manifolds, (with Raphael Zentner) Q. J. Math. 2010 62(2): 433-450.
A slice-genus lower bound from sl(n) Khovanov-Rozansky homology, Adv. Math. 2009 222(4): 1220-1276.



Juvenilia

On S.P numbers (with Paul Belcher, H.J. Godwin, Nick Lord, K. Robin McLean, and Phillip Williams) Math. Gaz. 82, (1998), 72-75
Deriving the nth Catalan number. Math. Gaz. 83 (1999), 109-110. .