My research interest lies in low-dimensional geometry and topology, and in particular in knots and links, 3-manifolds, and 4-manifolds. The tools I am interested in come from gauge theory, and in particular Donaldson- and Seiberg-Witten theory, Floer-homology, and representation varieties.
Here is a list of my articles all of which can also be found on the arXiv:
- Rational homology ribbon cobordism is a partial order (with Stefan Friedl and Filip Misev), preprint (2022), arXiv:2204.10730
- The Montesinos trick for proper rational tangle replacement (with Duncan McCoy), preprint (2021), arXiv:2110.15106
- Toroidal integer homology three-spheres have irreducible SU(2)-representations (with Tye Lidman and Juanita Pinzon-Caicedo), preprint (2021), arXiv:arXiv:2101.02621
- A new algorithm for 3-sphere recognition (with Michael Heusener), preprint (2016), arXiv:1610.04092
Published or accepted
- Surgery obstructions and character varieties (with Steven Sivek), Trans. Amer. Math. Soc. 375 (2022), no. 5, 3351--3380. arXiv:1912.01866
- A menagerie of SU(2)-cyclic 3-manifolds (with Steven Sivek), Int. Math. Res. Notices, rnaa330, https://doi.org/10.1093/imrn/rnaa330, arXiv:1910.13270
- SU(2)-cyclic surgeries and the pillowcase (with Steven Sivek), accepted for publication in J. Differential Geom., arXiv:1710.01957
- On spectral sequences from Khovanov homology (with Andrew Lobb), Algebr. Geom. Topol. 20 (2020), no. 2, 531--564.
- Khovanov width and dealternation number of positive braid links (with Sebastian Baader, Peter Feller and Lukas Lewark), Math. Res. Lett. Vol. 26, no. 3 (2019), 627--641.
- Integer homology 3-spheres admit irreducible representations in SL(2,C), Duke Math. J. 167 (2018), no. 9, 1643--1712.
- Alternating number of torus knots with small braid index (with Peter Feller and Simon Pohlmann), Indiana Univ. Math. J. 67 (2018), 645--655.
- Knot concordances and alternating knots (with Stefan Friedl and Charles Livingston), Michigan Math. J. 66 (2017), no. 2, 421--432.
- A class of knots with simple SU(2)-representations, Selecta Math. 23 (2017), no. 3, 2219--2242.
- A vanishing result for a Casson-type instanton invariant, Proc. London Math. Soc. 109 (2014), no. 6, 1507--1548.
- The quantum sl(n) graph invariant and a moduli space
(with Andrew Lobb),
Int. Math. Res. Notices (2014), no. 7, 1956--1972.
- Integrable almost complex structures in principal bundles and holomorphic curves, Manuscripta Math. 141 (2013), no. 1, 211--239.
- On higher rank instantons & the monopole cobordism program, Quart. J. Math. 63 (2012), no. 1, 227--256.
- Representation spaces of pretzel knots, Algebr. Geom. Topol. 11 (2011), no. 5, 2941--2970.
- On Casson-type instanton moduli spaces over negative definite four-manifolds (with Andrew Lobb), Quart. J. Math. 62 (2011), no. 2, 433--450.
- A note on Logarithmic Transformations on the Hopf surface, C. R. Math. Acad. Sci. Paris 342 (2006), no. 1, 37--42.
- The influence of varus and valgus deviation on patellar kinematics in healthy knees: An exploratory cadaver study, (Michael Worlicek, Benedikt Moser, Günther Maderbacher, Raphael Zentner, Florian Zeman, Joachim Grifka, Armin Keshmiri), The Knee (2017), Volume 24, Issue 4, Pages 711--717.