Seminar series
Date
Fri, 17 May 2024
Time
15:00 -
16:00
Location
L5
Speaker
Kelly Spry Maggs
Organisation
École Polytechnique Fédérale de Lausanne (EPFL)
One-parameter persistence and rational homotopy theory are two different ‘torsion-free’ algebraic models of space. Each enhances the cochain complex with additional algebraic structure— persistence equips cochain complexes with an action of a polynomial coefficient ring; rational homotopy theory equips cochains complexes with a graded-commutative product.
The persistent minimal model we introduce in this talk reconciles these two types of algebraic structures. Generalizing the classical case, we will describe how persistent minimal models are built by successively attaching the persistent rational homotopy groups into the persistent CDGA model. The attaching maps dualize to a new invariant called the persistent rational k-invariant.
This is joint work with Samuel Lavenir and Kathryn Hess: https://arxiv.org/abs/2312.08326