# Michael Lesnick : Interleavings and Multi-parameter Persistent Homology

**Time: **
Tue 2019-05-28 11.15 - 12.15

**Location: **
Place: Room 3418, math department KTH, floor 4 (bottom floor)

**Participating: **
Michael Lesnick, SUNY

Abstract: In topological data analysis (TDA), we associate to data a diagram of topological spaces, which we then study using algebraic topology. Topologists have been studying diagrams of topological spaces for decades; mathematically, what sets TDA apart from classical work is that in TDA, we are interested primarily in *approximate relations* between diagrams of spaces and their invariants, rather than in exact relations. For example, we are typically more interested in whether two diagrams of spaces are close to one another in some suitably chosen metric than whether they are isomorphic (or weakly equivalent) on the nose. Much of my recent work has focused on

*interleavings*, which have emerged as the formal language of choice in TDA for expressing such approximate relations. I've been especially interested in interleavings in the setting of multi-parameter persistent homology, where they can be used to formulate multi-parameter versions of fundamental stability and inference results in TDA. In this talk, I'll introduce interleavings and multi-parameter persistent homology, and discuss some recent results about these.