@article{22291,
  abstract     = {Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute invariant known as the persistence diagram. However, this is no longer the case for maps between persistence modules (i.e. persistence maps). We propose a new invariant for persistence maps, consisting of a partial matching between the persistence diagrams of the domain and codomain modules. We show that this invariant is additive with respect to the direct sum decomposition of persistence maps, is more discriminative than the image module, and is computable in cubic time. Furthermore, we provide an implementation and demonstrate its efficiency by integrating it with edge collapse techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical contribution, we describe how to induce a persistence map between two flag complexes that have been independently simplified via edge collapses, even when a direct simplicial map between them is no longer available.},
  author       = {Gonzalez-Diaz, Rocio and Soriano Trigueros, Manuel and Torras-Casas, Alvaro},
  issn         = {1095-855X},
  journal      = {Journal of Symbolic Computation},
  keywords     = {Persistence module, Persistence map, Persistent homology},
  publisher    = {Elsevier},
  title        = {{Additive partial matchings induced by persistence maps}},
  doi          = {10.1016/j.jsc.2026.102598},
  volume       = {138},
  year         = {2026},
}

@article{17437,
  abstract     = {We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were introduced by Budur. We also transfer the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau categories, based on recent work of Davison. This has interesting arithmetic applications on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptotic behaviour of counts of jets of quiver moment maps over finite fields. Moreover, we interpret the limit of counts of jets on a given moduli space as its p-adic volume under a canonical measure analogous to the measure built by Carocci, Orecchia and Wyss on certain moduli spaces of coherent sheaves.},
  author       = {Vernet, Tanguy},
  issn         = {1531-586X},
  journal      = {Transformation Groups},
  pages        = {1047--1083},
  publisher    = {Springer Nature},
  title        = {{Rational singularities for moment maps of totally negative quivers}},
  doi          = {10.1007/s00031-024-09873-0},
  volume       = {31},
  year         = {2026},
}