About me

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.


Click here to learn more about me.


This year I am not teaching any class. Click here for my past teaching.



  1. Splitting links by integer homology spheres (with Marco Golla). arXiv link
  2. Smoothly slice links in S^2 x S^2 and CP^2 # \overline{CP^2} (with Clayton McDonald). arXiv link
  3. On the rank of knot homology theories and concordance (with Nathan M. Dunfield, Sherry Gong, Thomas Hockenhull, and Michael Willis). arXiv link
  4. Unknotting number 21 knots are slice in K3 (with Stefan Mihajlović). arXiv link

Accepted for publication

  1. 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


  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

Other manuscripts


  1. Spectra in Khovanov and knot Floer theories (with Sucharit Sarkar and András Stipsicz). To appear in Singularities and Low Dimensional Topology, Bolyai Society Mathematical Studies. arXiv link

M.Sc. thesis

  1. On infinite families of non-quasi-alternating thin knots. PDF
    This is a largely expository work, written in 2013.
    WARNING: I was not familiar with citing conventions back then, so sadly you will not find proper references for theorems, propositions, and parts of the expositions.


Past teaching at UCLA

Term Classes taught
Spring 2020 MATH 123 - Foundations of Geometry
Winter 2020 MATH 31B - Integration and infinite series
Fall 2019 MATH 31B - Integration and infinite series
MATH 115A - Linear Algebra
Spring 2019 MATH 31B - Integration and infinite series
MATH 123 - Foundations of Geometry
Winter 2019 MATH 31B - Integration and infinite series
Fall 2018 MATH 115A - Linear Algebra
MATH 235 - Manifold Theory
Spring 2018 MATH 115A - Linear Algebra
MATH 131A - Analysis
Winter 2018 MATH 115B - Linear Algebra
MATH 123 - Foundations of Geometry
Fall 2017 MATH 31B - Integration and infinite series


  • Address

    Alfréd Rényi Institute of Mathematics
    Reáltanoda utca 13-15, 1053 Budapest, Hungary
  • Email

    mysurname@renyi.hu (after replacing "mysurname" with my surname)