Rate My Professor Daniele Celoria

Celoria's specific research areas include quantum invariants of 3-manifolds, knot homologies especially concerning concordances and 4-dimensional smooth topology, connections between discrete structures such as matchings and discrete Morse functions and their smooth counterparts via combinatorial algebraic topology, and applications of topological data analysis techniques to knot theory. He is available for supervision of higher degree by research students and currently acts as Associate Advisor on the Doctor of Philosophy project titled "Efficient algorithms in three-dimensional topology," with primary advisors Professor Benjamin Burton and Dr. Agnese Barbensi. His scholarly output comprises 18 publications spanning 2015 to 2026. Key works include "An exploration of low crossing and chiral cosmetic bands with grid diagrams" (Experimental Mathematics, 2026, with Barbensi et al.); "From the Mayer-Vietoris spectral sequence to überhomology" (Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2025, with Caputi and Collari); "GridPyM: a Python module to handle grid diagrams" (Journal of Software for Algebra and Geometry, 2024, with Barbensi); "Monotone cohomologies and oriented matchings" (Homology, Homotopy and Applications, 2024, with Caputi and Collari); "Categorifying connected domination via graph überhomology" (Journal of Pure and Applied Algebra, 2023, with Caputi and Collari); "Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology" (Science Advances, 2020, with Barbensi et al.); "The Reidemeister graph is a complete knot invariant" (Algebraic and Geometric Topology, 2020, with Barbensi); "Heegaard Floer homology and concordance bounds on the Thurston norm" (Transactions of the American Mathematical Society, 2020, with Golla and Levine); and "On concordances in 3-manifolds" (Journal of Topology, 2018). These publications contribute significantly to advancements in low-dimensional topology and interdisciplinary applications, such as DNA topology modeling.