Discrete Morse Theory Meets Multi-Parameter Persistence

Explore the intersection of Discrete Morse Theory and Multi-Parameter Persistence in this 52-minute lecture by Claudia Landi. Delve into how Discrete Morse theory reduces cell complexes to critical cells, carrying essential homological information. Examine the potential of multiparameter persistence in topological data analysis for multivariate data, while addressing its computational challenges. Learn about recent collaborative research findings, including the sufficiency of critical cell entrance values in determining the fibered rank invariant, the acceleration of multi-parameter persistence computation through Morse complex reduction, and the derivation of Morse inequalities for Betti numbers in multi-parameter persistence modules. Gain insights into the ongoing efforts to bridge these two theories and their implications for advancing topological data analysis.