David Trotman

Friday, December 6th,2019. Room 4-001 , at 4:00 p.m

**Title: Some geometric properties of Whitney stratified sets**

**Abstract: **In 1965 Whitney introduced conditions (a) and (b) on a stratification

of an analytic variety, ensuring stability of transversality to strata and constance

of the local topological type near a stratum. We discuss geometric properties

of smooth Whitney stratified sets and possible improvements, in particular to

the local bilipschitz type of definable sets in o-minimal structures. We describe

recent refinements of the Thom-Mather isotopy theorem, and an application to

Whitney cellulation of Whitney stratified sets which implies the proof of a 1981

homology conjecture of Goresky.