I am currently a Postdoctoral Research Assistant at the University of Oxford, under the supervision of Prof. András Juhász. I completed a thesis on "Grid homology in lens spaces" under the supervision of Prof. Paolo Lisca.

I am interested in low dimensional topology, with a focus on knot theory and its many
connections with the topology of 3 and 4 dimensional manifolds.
My current work revolves around Khovanov and Knot Floer homologies,
especially Grid Homology in lens spaces and applications to concordances.

email: Daniele.celoria  [AT] maths.ox.ac.uk or celoria  [AT] mail.dm.unipi.it

With Daniele Cappelletti in Copenaghen
picture courtesy of Arne Barbe


Cuspidal curves and Heegaard Floer homology (joint work with József Bodnár and Marco Golla)
[Abstract] [pdf] Proc. London Math. Soc. (2016) 112 (3): 512-548.

A note on cobordisms of algebraic knots (joint work with József Bodnár and Marco Golla)
[Abstract] [pdf] Accepted (AGT).

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

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

On concordances in 3-manifolds
[Abstract] [pdf] Submitted.

The Reidemeister graph (joint work with Agnese Barbensi)
[Abstract] Preprint available upon request.

Some seminars and talks:

"Introduction to Khovanov homology" (Pisa)

"Elliptic surfaces and rational blowdown" (Pisa)

"Un invariante di concordanza per nodi dalle chirurgie di Dehn" (Pisa)

"Grid homology in lens spaces" (Bologna). Slides

"An introduction to Grid homology", minicourse (Pisa)

"Grid homology in lens spaces: coeffcients and computations" (CIRM). Slides

"Concordances in 3-manifolds" (SNS - Pisa- Lille).

"Concordances and HFK" Slides (from ECSTATIC 2016).

"Khovanov-Floer Theories" (University of Oxford).

"Some concordance invariants from knot Floer homology" (University of Oxford). Slides and grid homology leaflet png

"Categorification of knot polynomials" North meets South Colloquium (University of Oxford). Slides

Attended schools and conferences


Here you can find some (hopefully!) useful programs I have been writing in during my Phd.

Click on the images to get redirected to a Sage script!

Grid homology calculator for knots in lens spaces

This program lets you draw grid diagrams

This program computes the Alexander polynomial of a 2-bridge knot or link,
and tells you if it is (smoothly) slice.

This program computes the number of homeomorphism classes of the lens spaces L(p,q) for fixed p.

This program computes the correction terms for lens spaces

This program computes the Alexander polynomial of a grid diagram in the 3-sphere

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!

About me

I was one of the organizers of the "Baby geometri" seminars at the University of Pisa.

I enjoy juggling any kind of objects, and thinking at all the math behind it.

I am a big fan of :

KnotAtlas KnotInfo

Curriculum Vitae (.pdf files):
Italiano English

Some friends/colleagues

Weird tree in Palermo
Trip to Lerici with unicycles
Pavement in Copenhagen
Making a new "black"board
On a beach in the Canary Islands
Another weird tree in Palermo!
Night in Copenhagen

This site is under constant maintenance! If something is not working properly do not hesitate to contact me!