Overview
Background
I am interested in low-dimensional geometric topology, with a focus on knot theory, quantum invariants of 3-manifolds, and knot homologies --especially in relation to concordances and 4-dimensional smooth topology. I recently got interested in the deep connections, usually provided by combinatorial algebraic topology, between discrete structures --such as matchings and discrete Morse functions-- and their smooth counterparts. As a side interest, I try to apply techniques from topological data analysis to knot theory.
Availability
- Dr Daniele Celoria is:
- Available for supervision
Fields of research
Qualifications
- Bachelor of Mathematics, Università di Pisa
- Masters (Research) of Mathematics, Università di Pisa
- Doctoral (Research) of Mathematics, Universita' di Firenze
Research interests
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Low-dimensional geometric topology
The study of manifolds in dimensions up to four, using algebraic, topological and gauge-theoretic techniques
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Knot theory
Study of mathematical knots through combinatorics and topology
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Cryptography
The art of establishing secure communications
Works
Search Professor Daniele Celoria’s works on UQ eSpace
2024
Journal Article
GridPyM: a Python module to handle grid diagrams
Barbensi, Agnese and Celoria, Daniele (2024). GridPyM: a Python module to handle grid diagrams. Journal of Software for Algebra and Geometry, 14 (1), 31-39. doi: 10.2140/jsag.2024.14.31
2024
Journal Article
MONOTONE COHOMOLOGIES AND ORIENTED MATCHINGS
Caputi, Luigi, Celoria, Daniele and Collari, Carlo (2024). MONOTONE COHOMOLOGIES AND ORIENTED MATCHINGS. Homology, Homotopy and Applications, 26 (2), 137-161. doi: 10.4310/HHA.2024.v26.n2.a7
2023
Journal Article
From the Mayer-Vietoris spectral sequence to überhomology
Caputi, Luigi, Celoria, Daniele and Collari, Carlo (2023). From the Mayer-Vietoris spectral sequence to überhomology. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. doi: 10.1017/prm.2023.104
2023
Journal Article
Categorifying connected domination via graph überhomology
Caputi, Luigi, Celoria, Daniele and Collari, Carlo (2023). Categorifying connected domination via graph überhomology. Journal of Pure and Applied Algebra, 227 (9) 107381, 107381. doi: 10.1016/j.jpaa.2023.107381
2023
Journal Article
A note on grid homology in lens spaces: coefficients and computations
Celoria, Daniele (2023). A note on grid homology in lens spaces: coefficients and computations. Glasgow Mathematical Journal, 65 (2), 457-479. doi: 10.1017/S0017089523000058
2023
Journal Article
Filtered simplicial homology, graph dissimilarity and überhomology
Celoria, Daniele (2023). Filtered simplicial homology, graph dissimilarity and überhomology. Journal of Algebraic Combinatorics, 57 (3), 859-904. doi: 10.1007/s10801-022-01205-3
2022
Journal Article
Filtered matchings and simplicial complexes
Celoria, Daniele and Yerolemou, Naya (2022). Filtered matchings and simplicial complexes. Australasian Journal of Combinatorics, 82 (3), 335-352.
2022
Journal Article
A statistical approach to knot confinement via persistent homology
Celoria, Daniele and Mahler, Barbara I. (2022). A statistical approach to knot confinement via persistent homology. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 (2261), 20210709. doi: 10.1098/rspa.2021.0709
2021
Journal Article
Upsilon invariants from cyclic branched covers
Alfieri, Antonio, Celoria, Daniele and Stipsicz, András (2021). Upsilon invariants from cyclic branched covers. Studia Scientiarum Mathematicarum Hungarica, 58 (4), 457-488. doi: 10.1556/012.2021.01515
2021
Journal Article
A discrete morse perspective on knot projections and a generalised clock theorem
Celoria, Daniele and Yerolemou, Naya (2021). A discrete morse perspective on knot projections and a generalised clock theorem. Electronic Journal of Combinatorics, 28 (3). doi: 10.37236/9979
2020
Journal Article
The Reidemeister graph is a complete knot invariant
Barbensi, Agnese and Celoria, Daniele (2020). The Reidemeister graph is a complete knot invariant. Algebraic and Geometric Topology, 20 (2), 643-698. doi: 10.2140/agt.2020.20.643
2020
Journal Article
Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology
Barbensi, Agnese, Celoria, Daniele, Harrington, Heather A., Stasiak, Andrzej and Buck, Dorothy (2020). Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology. Science Advances, 6 (9) eaay1458, 1-8. doi: 10.1126/sciadv.aay1458
2020
Journal Article
Heegaard floer homology and concordance bounds on the Thurston norm
Celoria, Daniele, Golla, Marco and Levine, Adam Simon (2020). Heegaard floer homology and concordance bounds on the Thurston norm. Transactions of the American Mathematical Society, 373 (1), 295-318. doi: 10.1090/tran/7906
2020
Journal Article
Rational cobordisms and integral homology
Aceto, Paolo, Celoria, Daniele and Park, Junghwan (2020). Rational cobordisms and integral homology. Compositio Mathematica, 1825-1845. doi: 10.1112/S0010437X20007320
2018
Journal Article
On concordances in 3-manifolds
Celoria, Daniele (2018). On concordances in 3-manifolds. Journal of Topology, 11 (1), 180-200. doi: 10.1112/topo.12051
2017
Journal Article
A note on cobordisms of algebraic knots
Bodnár, József, Celoria, Daniele and Golla, Marco (2017). A note on cobordisms of algebraic knots. Algebraic and Geometric Topology, 17 (4), 2543-2564. doi: 10.2140/agt.2017.17.2543
2015
Journal Article
Cuspidal curves and Heegaard Floer homology
Bodnár, József, Celoria, Daniele and Golla, Marco (2015). Cuspidal curves and Heegaard Floer homology. Proceedings of the London Mathematical Society, 112 (3), 512-548. doi: 10.1112/plms/pdv074
Supervision
Availability
- Dr Daniele Celoria is:
- Available for supervision
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