Marco Marengon
Senior Research Fellow
Alfréd Rényi Institute of Mathematics

I am a senior research fellow at the Alfréd Rényi Institute of Mathematics working in low-dimensional topology.
My research interests include knot concordance, link cobordisms, embedded surfaces in 4-manifolds, and Heegaard Floer homology.

We are hiring!

We have an open 2-year postdoc position in low-dimensional topology at the Rényi Institute. The deadline for application is 31st January 2025. Click here for more information.
There is also a generic postdoc position for all areas of Mathematics, called the Rényi Postdoctoral Fellowship: click here for more information.

Research

Preprints

1. Correction terms of double branched covers and symmetries of immersed curves (with Jonathan Hanselman and Biji Wong). arXiv link
2. Splitting links by integer homology spheres (with Marco Golla). arXiv link
3. Smoothly slice links in S^2 x S^2 and CP^2 # \overline{CP^2} (with Clayton McDonald). arXiv link
4. On the rank of knot homology theories and concordance (with Nathan M. Dunfield, Sherry Gong, Thomas Hockenhull, and Michael Willis). arXiv link

Accepted for publication

1. Unknotting number 21 knots are slice in K3 (with Stefan Mihajlović). To appear in Mathematical Research Letters. arXiv link
2. A note on surfaces in CP^2 and CP^2 # CP^2 (with Allison N. Miller, Arunima Ray, and András I. Stipsicz). To appear in Proceedings of the AMS. arXiv link

Publications

1. Relative genus bounds in indefinite four-manifolds (with Ciprian Manolescu and Lisa Piccirillo). Mathematische Annalen (2024). Published version arXiv link
2. Non-orientable link cobordisms and torsion order in Floer homologies (with Sherry Gong). Algebraic & Geometric Topology 23, iss. 6 (2023), 2627-2672. DOI arXiv link
3. A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds (with Ciprian Manolescu, Sucharit Sarkar, and Michael Willis). Duke Mathematical Journal 172, iss. 2 (2023), 231–311. DOI arXiv link
4. Strands algebras and Ozsváth-Szabó's Kauffman-states functor (with Andrew Manion and Michael Willis), Algebraic & Geometric Topology 20, iss. 7 (2020), 3607-3706. DOI arXiv link
5. Generators, relations, and homology for Ozsváth-Szabó's Kauffman-states algebras, (with Andrew Manion and Michael Willis), Nagoya Mathematical Journal (2020), 1-59. DOI arXiv link
6. The Knight Move Conjecture is false (with Ciprian Manolescu), Proceedings of the American Mathematical Society 148 (2020), 435-439. DOI arXiv link
7. Correction terms and the non-orientable slice genus (with Marco Golla), Michigan Mathematical Journal 67, iss. 1 (2018), 59-82. DOI arXiv link
8. Computing cobordism maps in link Floer homology and the reduced Khovanov TQFT (with András Juhász), Selecta Mathematica, New Series 24 (2018), 1315-1390. DOI arXiv link
9. Concordance maps in knot Floer homology (with András Juhász), Geometry & Topology 20 (2016), 3623-3673. DOI arXiv link
10. On d-invariants and generalised Kanenobu knots, Journal of Knot Theory and Its Ramifications 25, iss. 8 (2016), 1650048. DOI arXiv link

Ph.D. thesis

1. Heegaard Floer homology and link cobordisms Mathematics PhD theses, Imperial College London (2017). DOI