Daniele Celoria

Postdoctoral Research Assistant
at the University of Oxford.

daniele.celoria -at- maths.ox.ac.uk

I like low-dimensional topology, especially knot theory.
My current work revolves around knot Floer homology,
and its applications to the study of concordances.


A list of my papers and preprints in pdf format


Here you can find some (hopefully!) useful programs I wrote using Sage


CV, teaching, slides and random stuff


links to useful resources and friends' homepages


Rational cobordisms and integral homology
(joint work with Paolo Aceto and JungHwan Park)

[Abstract] [pdf] Preprint (2018).

Upsilon invariants from cyclic branched covers
(joint work with Antonio Alfieri and Andras Stipsicz)

[Abstract] [pdf] Preprint (2018).

Heegaard Floer homology and concordance bounds on the Thurston norm
(joint work with Marco Golla)

[Abstract] [pdf] Preprint (2018).

The Reidemeister graph is a complete knot invariant
(joint work with Agnese Barbensi)

[Abstract] [pdf] Submitted (2018).

On concordances in 3-manifolds
[Abstract] [pdf] Journal of Topology 11.1 (2018).

A note on cobordisms of algebraic knots
(joint work with József Bodnár and Marco Golla)

[Abstract] [pdf] AGT., vol 17 n.4 (2017).

Cuspidal curves and Heegaard Floer homology
(joint work with József Bodnár and Marco Golla)

[Abstract] [pdf] Proc. London Math. Soc. (2016) 112 (3).

Grid homology in lens spaces
[Abstract] [pdf] Ph.D. Thesis (2016).

Grid homology in lens spaces with integer coefficients
[Abstract] [pdf] arXiv preprint (2015).

Image from Seifert view


If the programs do not start, try pressing Ctrl + Shift + R. You can also download the programs and use them on your local Sage distribution.

Soon other programs will be added! All the programs are released under a GNU General Public Licence. Practically this means that you can use or modify them as you please, according to the copyleft model. Let me know if you encountered problems using them, or if you have suggestions!


Ask me about this picture!

  • Useful links and computational tools:

  • Sage: a free open-source mathematics software system licensed under the GPL.
  • Mathoverflow: a question and answer site for professional mathematicians.
  • KnotAtlas: a complete user-editable knot atlas, in the wiki spirit of Wikipedia.
  • KnotInfo: pre-computed knot and link invariants
  • KnotPlot: a collection of knots and links, viewed from a (mostly) mathematical perspective
  • Kirby Calculator: a program that lets you draw and manipulate Kirby diagrams
  • Seifertview: with this tool a variety of knots and links in many different styles
  • Gridlink: a tool for manipulating the rectangular link diagrams
  • Sci-Hub: (better use a VPN for this one!)
  • Knot identification tool:: a handy way to check knot types online