# 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 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).

*From the Mayer-Vietoris spectral sequence to überhomology*. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. doi: 10.1017/prm.2023.104
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). 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) ARTN eaay1458, 1-8. doi: 10.1126/sciadv.aay1458
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
Aceto, Paolo, Celoria, Daniele and Park, Junghwan (2020).

*Rational cobordisms and integral homology*. Compositio Mathematica, 1825-1845. doi: 10.1112/S0010437X20007320
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