I am a mathematician working in lowdimensional topology.
My research interests include knot concordance, link cobordisms, embedded surfaces in 4manifolds, and Heegaard Floer homology.
Since September 2021 I am at the Alfréd Rényi Institute of Mathematics.
I am coorganising 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.
Check out this upcoming Lowdimensional workshop, which will take place at the Rényi Institute on 2731 March 2023.
Click here to learn more about me.
Click here for a list of my publications.
This year I am not teaching any class. Click here for my past teaching.
Click here for my work address and email.
Research
Preprints

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 fourmanifolds
(with Ciprian Manolescu and Lisa Piccirillo).
arXiv link
Accepted for publication

Nonorientable link cobordisms and torsion order in Floer homologies
(with Sherry Gong). To appear in Algebraic & Geometric Topology.
arXiv link
Publications

A generalization of Rasmussen's invariant, with applications to surfaces in some fourmanifolds
(with Ciprian Manolescu, Sucharit Sarkar, and Michael Willis).
Duke Mathematical Journal 172, iss. 2 (2023), 231–311.
DOI
arXiv link

Strands algebras and OzsváthSzabó's Kauffmanstates functor
(with Andrew Manion and Michael Willis),
Algebraic & Geometric Topology 20 (2020), 36073706.
DOI
arXiv link

Generators, relations, and homology for OzsváthSzabó's Kauffmanstates algebras,
(with Andrew Manion and Michael Willis),
Nagoya Mathematical Journal (2020), 159.
DOI
arXiv link

The Knight Move Conjecture is false
(with Ciprian Manolescu),
Proceedings of the American Mathematical Society 148 (2020), 435439.
DOI
arXiv link

Correction terms and the nonorientable slice genus
(with Marco Golla),
Michigan Mathematical Journal 67, iss. 1 (2018), 5982.
DOI
arXiv link

Computing cobordism maps in link Floer homology and the reduced Khovanov TQFT
(with András Juhász),
Selecta Mathematica, New Series 24 (2018), 13151390.
DOI
arXiv link

Concordance maps in knot Floer homology
(with András Juhász),
Geometry & Topology 20 (2016), 36233673.
DOI
arXiv link

On dinvariants and generalised Kanenobu knots,
Journal of Knot Theory and Its Ramifications 25, iss. 8 (2016), 1650048.
DOI
arXiv link
Ph.D. thesis

Heegaard Floer homology and link cobordisms
Mathematics PhD theses, Imperial College London (2017).
DOI
Other manuscripts
M.Sc. thesis

On infinite families of nonquasialternating 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.
Teaching
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 