Explore methods for multiple hypothesis testing in persistent homology in this 57-minute conference talk by Mikael Vejdemo-Johansson. Delve into techniques for correcting family-wise error rates when testing against null models and false discovery rates in various settings. Discover the application of these multiple testing paradigms to post-hoc validation of Mapper complexes. Learn about joint work with Sayan Mukherjee that builds upon Cericola et al's research on ANOVA-type persistent homology tests. Gain insights into this developing area of applied algebraic topology and its potential implications for data analysis and topological data science.