TTT108: Sheffield

The University of Sheffield.

Supported by the London Mathematical Society.

Date

31 October 2018

Speakers

Michael Ching (Amherst College)
Pro-operads and Taylor towers of spectrum-valued functors

Abstract: In previous work with Greg Arone, we showed that the Goodwillie derivatives of a functor from based spaces to spectra form a module over a certain 'pro-operad' formed from the sequence of Koszul duals of the little disc operads. In this talk I will explain how to generalise that picture to functors on other ∞-categories. The main example I have in mind is algebraic K-theory as a functor of A_∞ ring spectra.

Xin Fu (Southampton)
Simplicial G-complexes and representation stability of polyhedral products

Abstract: With a simplicial G-complex K and a topological pair (X, A), a polyhedral product (X, A)K is associated as a G-invariant subspace of a product space. In this talk, we discuss the existence of a G-equivariant homotopy decomposition of its suspension ∑(X, A)K which further sets up the ground to study the notion of representation stability introduced by Benson and Church in toric topology. This is a joint work with Jelena Grbić.

Lukas Brantner (Oxford)
Formal moduli problems via partition Lie algebras 

Abstract: If k is a field of characteristic zero, a theorem of Lurie and Pridham establishes an equivalence between formal moduli problems and differential graded Lie algebras over k. We generalise this equivalence in two different ways to arbitrary ground fields by using 'partition Lie algebras'.

These mysterious new gadgets are intimately related to the genuine equivariant topology of the partition complex, which allows us to access the operations acting on their homotopy groups (relying on earlier work of Dyer-Lashof, Priddy, Goerss, and Arone-B.). This is joint work with Mathew.