Geometrical and Topological Methods for Computer Graphics

Yann-Situ Gazull (LIS)

This talk follows that of Alexandra Bac (on computational homology). Depending on the "choices" of participants, Yann-Situ Gazull can elaborate on:

• HDVSs (how to move from one HDVF to another through HDVFs operations, connectedness of HDVFs space, equivalence between HDVFs and state-of-art methods (SNF, persistent homology, tri-partitions).
• Homology bases "that can be computed". In a recent result, we have proved that only specific bases can be computed by state-of-art methods and we characterized them (explicit bases).
• Constructive Alexander duality. Another result, based on HDVFs, give a new (constructive) proof of Alexander isomorphism between the homology of an object and that of its complementary in S^n. HDVFs provide the isomorphism.
• Homological configurations (works in progress...). Starting from previous works, Yann-Situ Gazull introduced a new notion, that of homological configurations, classifying HDVFs (ie. homology computations) over a given object. These configurations are not homotopy invariants but they provide an interesting tool to analyse the topology/geometry link.

To discuss after March 31st 2025 session...