Effective Computation of Spectral Systems and Relation With Multi-Parameter Persistence

Explore the effective computation of spectral systems and their relation to multi-parameter persistence in this 50-minute conference talk by Ana Romero from the Applied Algebraic Topology Network. Delve into the world of Computational Algebraic Topology, focusing on algorithms and programs for computing spectral systems. Learn about the new module implemented for the Kenzo system that solves classical problems of spectral sequences, including differential maps and extensions. Discover how the combination of these programs with effective homology enables the computation of spectral systems for large, sometimes infinite-type spaces. Examine the connection between spectral systems and multi-parameter persistence, and understand how this relationship has led to enhanced programs capable of computing multi-parameter persistence invariants in a generalized framework, including spaces of infinite type. Gain insights from joint works with A. Guidolin, J. Divasón, and F. Vaccarino in this comprehensive exploration of advanced topological computations.