Title : « Theoretical foundations of persistence theory »
Abstract : « How to measure the underlying topological structure of a data set (seen as a point cloud in a metric space) ? How to characterize its sensibility to the choice of the scale we study it with ? Since the late 2000’s, computable and stable topological descriptors have been developed to partially answer this question. The theoretical foundations they rely on (namely, persistence theory) have opened new questions in algebraic topology that offers interesting perspectives for applications to analyze complex data sets. We propose to first motivate and explain those constructions in the well understood case of persistence with one parameter. In a second time, we will present some recent results in the difficult study of persistence with many parameters. «
- Monday : « An ode to topological data analysis : how and why ? » (Steve)
- Tuesday : « Persistence theory with one parameter : structure, decomposition and stability » (Nicolas and Steve)
- Wednesday : « Persistence theory with many parameters : why is it useful ? why is it difficult ? » (Steve and Nicolas)
- Thursday : « 1- Decomposition and stability for exact bi-modules 2- A derived approach to persistence theory » (Steve and Nicolas)
- Friday : « Persistence and sheaf theory » (Nicolas)
Prerequisite: linear algebra, commutative rings, modules.
rooms for the course
- 15h-17h, 12.03.2018 MNO 1.020
- 10h-12h, 13.03.2018 MNO 1.050
- 10h-12h, 14.03.2018 MSA 3.230
- 10h-12h, 15.03.2018 MNO 1.050
- 10h-12h, 16.03.2018 MSA 3.200