TTT114: Online
Hosted by Liverpool

Talks were online, using Zoom. We used Gather.town for discussions during the break and after the talks.

Date

29 March 2021

Speakers

Alice Hedenlund (Oslo)
Multiplicative spectral sequences via décalage

Abstract: Décalage was originally introduced by Deligne and one can roughly describe the process as providing us with a way to encode "turning the page of a spectral sequence" on the level of filtrations.

Although not originally phrased in this way, décalage can be made sense in terms taking connective covers of a filtration in a certain t-structure on the category of filtered complexes called the Beilinson t-structure. This allows one to generalise the construction also to filtered objects in other stable oo-categories, such as spectra.

In this talk, we show that the language of the Beilinson t-structure and décalage provides access to highly structured results on filtered spectra and their associated spectral sequences. In particular, we sketch how it can be used to show that the functor assigning a spectral sequence to a filtered spectrum can be endowed with the structure of a map of oo-operads.

Sylvain Douteau (L’Institut de Recherche En Informatique Fondamental, Paris)
Stratified homotopy theory

Abstract: Stratified spaces appear naturally in singularity theory. In the 80s, Goresky and Mac Pherson introduced intersection cohomology to generalise the cohomological properties of manifolds to some well-behaved stratified objects: the pseudo-manifolds. But intersection cohomology is not compatible with classical homotopy theory. This motivates the development of a new homotopy theory, better suited for the study of stratified spaces.

In this talk, after giving a quick review of some classical results in homotopy theory that we intend to generalise, I will present two approaches to the problem of constructing a stratified homotopy theory: one simplicial, and one topological. I will explain how these two compare to each other and to the standard case, and present a new invariant of stratified spaces: the stratified homotopy groups.

David Chataur (Amiens)
Blown-up cochains from an homotopical viewpoint

Abstract: In this talk, we plan to survey some recent results and joint works with M Saralegui and D Tanré about intersection cohomology in a simplicial framework. In particular, we will explain how intersection cohomology fits into the realm of stratified homotopy theory.

This homotopical treatment naturally leads to revisit some constructions in intersection cohomology but also to the construction of new topological invariants for pseudomanifolds.