Currently, my research focuses on knotted surfaces and 4-manifolds.
This note contains a description for non-mathematicians and a discussion of my (non-) usage of AI.
Publications and preprints
Homeomorphisms of surfaces in 4-manifolds, with Daniel Kasprowski.
Algebraic concordance of links, with David Cimasoni and Gaëtan Simian.
Non-smoothable surfaces in the 4-sphere, with Daniel Galvin.
Involutions on S^4, with Keegan Boyle and Wenzhao Chen.
4-manifolds with a given boundary, with Daniel Kasprowski.
The first relative k-invariant, with Daniel Kasprowski. Homol. Homotopy. Appl.
Simply slicing knots, with Patrick Orson and Mark Pencovitch.
Immersed surfaces with knot group Z, with Allison Miller.
Z-discs in CP^2, with Irving Dai and Maggie Miller, Compos. Math. 161 (2025), 1357 - 1403
Locally flat simple spheres in CP^2, with Patrick Orson, Bull. Lond. Math. Soc. 1 (2025) 150-163.
A criterion for double sliceness, New York J. Math. 30 (2024), 1079–1099.
Unknotting nonorientable surfaces, with Patrick Orson and Mark Powell. J. Eur. Math. Soc.
Infinite homotopy stable class for 4-manifolds with boundary, with Diarmuid Crowley and Mark Powell Pac. J. Math, 325 (2023), 209-237.
4-manifolds with boundary and fundamental group Z, with Lisa Piccirillo and Mark Powell. Comment. Math. Helv, 100 (2025), 323-420.
Homotopy ribbon discs with a fixed group, Algebr. Geom. Topol. 24 (2024), 4575-4587.
Stably diffeomorphic manifolds and the realisation of modified surgery obstructions, with Diarmuid Crowley, Mark Powell and Joerg Sixt. Mém. Soc. Math. Fr.
Simply-connected manifolds with large homotopy stable classes, with Diarmuid Crowley, Mark Powell and Joerg Sixt, J. Aust. Math. Soc. 115 (2023), 172-203.
Abelian invariants of doubly slice links, with Patrick Orson, Enseign. Math. 68 (2022), 243-290.
Embedded surfaces with infinite cyclic knot group, with Mark Powell, Geom. Topol. 27 (2023), 739-821; erratum.
Twisted signatures of fibered knots, with Matthias Nagel, Algebr. Geom. Topol 21 (2021) 1973-2036.
A note on the weak splitting number, with Alberto Cavallo and Carlo Collari, Proc. Amer. Math. Soc. 149 (2021), 1305-1321.
Non-slice linear combinations of iterated torus knots, with Min Hoon Kim and Wojciech Politarczyk Algebr. Geom. Topol 23 (2023). 765-802.
Characterisation of homotopy ribbon discs, with Mark Powell, Adv. Math. 391 (2021), Paper No. 107960.
Stably slice disks of links, with Matthias Nagel, J. Topol. 13 (2020), 1261-1301
Twisted Blanchfield pairings and twisted signatures III: Applications, with Maciej Borodzik and Wojciech Politarczyk, Glasgow Math. J. 66 (2024), 501-540.
Twisted Blanchfield pairings and twisted signatures II: Relation to Casson-Gordon invariants, with Maciej Borodzik and Wojciech Politarczyk. J. Inst. Math. Jussieu. 24 (2025) 1139-1195.
Twisted Blanchfield pairings and twisted signatures I: Algebraic background, with Maciej Borodzik and Wojciech Politarczyk, Linear. Algebra. Appl. 655 (2022) 236-290.
A multivariable Casson-Lin type invariant, with Léo Bénard, Ann. Inst. Fourier 70 (2020), 1029-1084.
Conway's potential function via the Gassner representation, with Solenn Estier, Asian J. Math. 24 (2020), 95-116.
Linking forms revisited, with Stefan Friedl and Gerrit Herrmann, Pure Appl. Math. Q. 12 (2018), 493-515.
An explicit computation of the Blanchfield pairing for arbitrary links, Can. J. Math. 70 (2018), 983-1007.
Multivariable signatures, genus bounds and 0.5-solvable cobordisms, with Matthias Nagel and Enrico Toffoli, Mich. Math. J. 69 (2020), 381-427.
The Blanchfield pairing of colored links, with Stefan Friedl and Enrico Toffoli, Indiana Univ. Math. J. 67 (2018), 2151-2180.
L^2-Burau maps and L^2-Alexander torsions, with Fathi Ben Aribi, Osaka J. Math. 55 (2018), 529-545.
A Burau-Alexander 2-functor on tangles, with David Cimasoni, Fund. Math. 240 (2018), 51-79.
Splitting numbers and signatures, with David Cimasoni and Kleopatra Zacharova, Proc. Amer. Math. Soc. 144 (2016), 5443-5455.
Burau maps and twisted Alexander polynomials, Proc. Edinburgh Math. Soc. 61 (2018) 479-497.
Coloured tangles and signatures, with David Cimasoni, Math. Proc. Cambridge Philos. Soc. 164 (2018), 493-530.
Other publications:
Classifying knotted surfaces (2026).
Stable homeomorphism and homotopy equivalence, Oberwolfach reports, report No. 4/2023, (2023), 22-26.
Invariants of 2-knots, (2022).
Locally flat surfaces in 4-manifolds, Oberwolfach reports, report No. 34/2022, (2022), 43-46.
The Levine-Tristram signature: a survey, 2019-20 MATRIX Annals, 4 (2021), 31-56.