I am currently a Postdoctoral Research Assistant at the University of Oxford, under the supervision of Prof. Andras Juhasz. 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 unifi.it* or *celoria mail.dm.unipi.it *

__Preprints __

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

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

**Grid homology in lens spaces with integer coefficients**

**Grid homology in lens spaces**

**On concordances in 3-manifolds**

**Some invariants of satellite operators**

**The Reidemeister graph** (*joint work with Agnese Barbensi*)

## 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).

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

## Attended schools and conferences

**Intensive Research Period "Knots and Applications"**, at the Centro De Giorgi, University of Pisa.**CAST Summer School and Conference**, at the Alfréd Rényi Institute of Mathematics in Budapest.**(u,v,w knots) x (topology, combinatorics, low and high algebra)**at the Centre for Quantum Geometry of Moduli Spaces, University of Aarhus.**Physics and Mathematics of Link Homology**, at the Centre de Recherche Mathèmatiques, Montreal.**Young Topologist Meeting**, at the Copenhagen University (there is also a nice group photo!).**10th William Rowan Hamilton Geometry and Topology Workshop**, Trinity College of Dublin.**XXII Gökova Geometry/Topology Conference**, Gökova, Turkey.**ECSTATIC 2015**, Imperial College, London.**Stein Manifolds, Contact Structures and Knots**, CIRM, Marseille.**Varieta' reali e complesse: geometria, topologia e analisi armonica**, SNS.-
**ECSTATIC 2016**Imperial College, London. -
**Perspectives in topology and geometry of 4-manifolds**I.U.C. Dubrovnik

# __Programs__

### 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!

####

**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 am 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 : **

Weird tree in Palermo
Trip to Lerici with unicycles
Pavement in Copenhagen
Piazza De Ferrari, Genova
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!