Click here for a list of my publications.
I am a mathematician working in low-dimensional topology. My research interests include knot concordance, link cobordisms, embedded surfaces in 4-manifolds, and Heegaard Floer homology. Since September 2021 I am at the Alfréd Rényi Institute of Mathematics.
I am co-organising a research semester in Singularities and Low Dimensional Topology at the Erdős Center in Budapest, from January 2023 to June 2023. The program includes a winter school and 3 research conferences. Registration for the Winter school in singularities and low dimensional topology is open until 31st October 2022.
- 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
Accepted for publication
- Non-orientable link cobordisms and torsion order in Floer homologies (with Sherry Gong). To appear in Algebraic & Geometric Topology. arXiv link
- A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds (with Ciprian Manolescu, Sucharit Sarkar, and Michael Willis). To appear in Duke Mathematical Journal. arXiv link
- Strands algebras and Ozsváth-Szabó's Kauffman-states functor (with Andrew Manion and Michael Willis), Algebraic & Geometric Topology 20 (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 (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, No. 08 (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|