Preprints
Polynomial inscriptions. (with Josh Greene).Square pegs between two graphs (with Josh Greene).Floer homology and square pegs (with Josh Greene).
Published or accepted papers
A feeling for Khovanov homology , to appear in Notices of the AMS. Squeezed knots , (with Peter Feller and Lukas Lewark), to appear in Quantum Topol.On the values taken by slice-torus invariants , (with Peter Feller and Lukas Lewark), Math. Proc. Cambridge Philos. Soc. 176(1) (2024) 55-63.Almost positive links are strongly quasipositive , (with Peter Feller and Lukas Lewark). Math. Ann. 385, 481-510 (2023). Cyclic quadrilaterals and smooth Jordan curves , (with Josh Greene). Invent. Math. 234(3) (2023) 931-935 [See also a chapter in What's Happening in the Mathematical Sciences, Volume 12 .]The rectangular peg problem , (with Josh Greene). Ann. of Math. 194 (2021) 509-517. [See also the Quanta Magazine article oder der Süddeutsche Zeitung artikel .]A refinement of Khovanov homology , (with Liam Watson). Geom. Topol. 25 (2021) 1861-1917. A calculus for flow categories , (with Patrick Orson and Dirk Schuetz). 409 (2022), 58 pp.A counterexample to Batson's conjecture. Math. Res. Lett. 26(6) 2019 1789-1789.An sl(n) stable homotopy type for matched diagrams , (with Dan Jones and Dirk Schuetz). Adv. Math. 356 (2019), 106816.On spectral sequences from Khovanov homology , (with Raphael Zentner). Algebr. Geom. Topol. 20 (2020) 531-564. On the functoriality of Khovanov-Floer theories , (with John Baldwin and Matt Hedden). Adv. Math. 2019 345: 1162-1205.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). Geom. Topol. 23 (2019) 745-780.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.Preprints not submitted for publication
The Dold-Whitney theorem and the Sato-Levine invariant. Non-pure papers
Threaded rings that swim in excitable media , (with Elizabeth Bromley, Brette Chapin, Antonio Cincotti, David Evans, Kate Horner, Fabian Maucher, Jonathan Steed, and Paul Sutcliffe). Phys. Rev. Lett. 123, 258102 (2019)Unknotting the interactive effects of learning processes
on cultural evolutionary dynamics. , (with Lauren Scanlon, Jeremy Kendal, and Jamie Tehrani). Evolutionary Human Sciences, vol 1 (2019).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 