I work around low-dimensional topology, which has to do with the properties of shapes we can (nearly) visualize, and usually with some influence from combinatorics, which has to do with the properties of discrete structures, like networks.
My papers on the arXiv. Eventually, I intend to include links to their available published versions, and in the meantime you can consult my CV to see where to find them.
I wrote a survey article on Heegaard Floer homology for the Notices of the American Mathematical Society (January 2021).
I am an editor at the (semi-new) journal Studia Scientiarum Mathematicarum Hungarica: Combinatorics, Geometry and Topology. Consider it for your "original research paper of high quality and significance specialized in combinatorics, and combinatorial aspects of geometry and topology!"
Slides (and some videos) from talks
Loops intersecting at most once. LA Joint Topology Seminar, Caltech. March 9, 2020.
Perspectives on Dehn surgery. Texas Geometry / Topology Conference, University of Texas, Austin. November 17, 2017.
Trees and Numbers. Navajo Nations Teacher Workshop. March 6, 2021 (not 202, as misdated on the actual slides...).
I maintain the pages for current and past graduate courses I have taught.
Spring 2021: Knot homology theories.
Fall 2021: Algebraic topology.
Spring 2021: Symplectic geometry and pseudoholomorphic curves.
Spring 2019: Combinatorial methods in low-dimensional topology.
Spring 2018: Graduate combinatorics.
Fall 2015: Introduction to knot theory.
Spring 2013: Combinatorial methods in knot theory.
Summer School and Book
I organized a graduate summer school entitled "Perspectives on Dehn Surgery'' at ICERM during the dates of July 15-19, 2019. The link will take you to video and other materials from the event, and a book based on the lecture series is in the works.