How to Write a Statistics Theorem for Topologists

One of Sayan’s legacies was his development of, and advocacy for, more statistical rigour in the world of TDA. Inspired by this goal I will give a crude (and idiosyncratic) introduction to writing a statistics theorem suitable for TDA. We will see some examples of Sayan’s work alongside two case studies I am currently working on. Case study one is kernel regression using persistence diagrams (joint with Saksham Aggarwal and James Nichols). Case study two is on learning Betti numbers of algebraic varieties (joint with Thomas Burnett and Martin Helmer).