Dr Daniele Celoria
Lecturer
School of Mathematics and Physics
+61 7 336 53425
Researcher biography
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.
Publications
Journal Articles
Barbensi, Agnese, Celoria, Daniele, Ktenidis, Christopher, Ichihara, Kazuhiro, Jong, In Dae and Teragaito, Masakazu (2026). An Exploration of Low Crossing and Chiral Cosmetic Bands with Grid Diagrams. Experimental Mathematics, 1-8. doi: 10.1080/10586458.2025.2595007
Caputi, Luigi, Celoria, Daniele and Collari, Carlo (2025). From the Mayer-Vietoris spectral sequence to überhomology. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 155 (2), 540-563. doi: 10.1017/prm.2023.104
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
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
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
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
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
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
Celoria, Daniele and Yerolemou, Naya (2022). Filtered matchings and simplicial complexes. Australasian Journal of Combinatorics, 82 (3), 335-352.
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
Celoria, Daniele and Yerolemou, Naya (2021). A discrete morse perspective on knot projections and a generalised clock theorem. Electronic Journal of Combinatorics, 28 (3) P3.3. doi: 10.37236/9979
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
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
Aceto, Paolo, Celoria, Daniele and Park, Junghwan (2020). Rational cobordisms and integral homology. Compositio Mathematica, 156 (9), 1825-1845. doi: 10.1112/S0010437X20007320
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
Celoria, Daniele (2018). On concordances in 3-manifolds. Journal of Topology, 11 (1), 180-200. doi: 10.1112/topo.12051
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
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