Click here for a list of my publications.
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.
- On the rank of knot homology theories and concordance (with Nathan M. Dunfield, Sherry Gong, Thomas Hockenhull, and Michael Willis). arXiv link
- A note on surfaces in CP^2 and CP^2 # CP^2 (with Allison N. Miller, Arunima Ray, and András I. Stipsicz). arXiv link
- Unknotting number 21 knots are slice in K3 (with Stefan Mihajlović). arXiv link
- Relative genus bounds in indefinite four-manifolds (with Ciprian Manolescu and Lisa Piccirillo). arXiv link
- 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
- 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
- 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
- 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
- The Knight Move Conjecture is false (with Ciprian Manolescu), Proceedings of the American Mathematical Society 148 (2020), 435-439. DOI arXiv link
- Correction terms and the non-orientable slice genus (with Marco Golla), Michigan Mathematical Journal 67, iss. 1 (2018), 59-82. DOI arXiv link
- 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
- Concordance maps in knot Floer homology (with András Juhász), Geometry & Topology 20 (2016), 3623-3673. DOI arXiv link
- On d-invariants and generalised Kanenobu knots, Journal of Knot Theory and Its Ramifications 25, iss. 8 (2016), 1650048. DOI arXiv link
- Heegaard Floer homology and link cobordisms Mathematics PhD theses, Imperial College London (2017). DOI
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
|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|