Nicolò Zava

I am a postdoctoral fellow at the Institute of Science and Technology Austria (ISTA) in Herbert Edelsbrunner's research group.

Previously, I was a postdoc at the University of Udine (Italy). I received my PhD at the University of Udine under the supervision of Dikran Dikranjan.

Research interests

My research lies in the interplay between metric geometry and computational topology. The latter field has experienced significant development over the past couple of decades, driven by its successful applications to real-world datasets and machine learning pipelines. Since many datasets can be modelled as metric spaces or generalisations thereof, metric geometry provides a natural theoretical framework for studying the properties of their computational invariants. In particular, I study the Gromov-Hausdorff distance for its role in comparing datasets and use dimension theory to discuss its complexity. The interaction between metric geometry and computational topology is also bidirectional: questions arising from applications in turn motivate the introduction of new concepts and techniques, including generalisations of the Gromov-Hausdorff distance.

Selected publications and preprints

N. Zava, Coarse and bi-Lipschitz embeddability of subspaces of the Gromov-Hausdorff space into Hilbert spaces, Algebr. Geom. Topol., to appear. arXiv:2303.04730v3 (was The Gromov-Hausdorff space is not coarsely embeddable into any Hilbert space)
A. Garber, Ž. Virk, N. Zava, On the metric spaces of lattices and periodic point sets. arXiv:2310.07594
T. Weighill, T. Yamauchi, N. Zava, Coarse infinite-dimensionality of hyperspaces of finite subsets, Eur. J. Math. 8 (2022), no. 1, 335-355.
D. Dikranjan, N. Zava, The impact of Pontryagin and Bohr's functors on large-scale properties of LCA groups, Topology Appl. 275 (2020), 107025.
D. Dikranjan, I. Protasov, K. Protasova, N. Zava, Balleans, hyperballeans, and ideals, Appl. Gen. Top. 20, no. 2 (2019), 431-447.
D. Dikranjan, N. Zava, Some categorical aspects of the coarse category, Topology Appl. 225 (2017), 164-194.

The complete list of my publications can be found on the Research tab.

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