TTT112: Warwick

University of Warwick.

Supported by the London Mathematical Society.

Date

16 January 2020

Speakers

Dan Graves (Sheffield)
Comparing gamma homology and symmetric homology

Gamma homology, as introduced by Robinson and Whitehouse, is a homology theory for commutative algebras with applications to stable homotopy theory. Symmetric homology, as defined by Fiedorowicz, is a homology theory for associative algebras and is related to the homology of certain infinite loop spaces.

In this talk I will describe a comparison map for the two theories in the case of an augmented, commutative algebra.

Emanuele Dotto (Warwick)
The Grothendieck-Witt theory of quadratic functors

The Grothendieck-Witt spectrum of a ring is an object constructed from the forms (quadratic, symmetric, or symplectic) on that ring, in a way analogous to Quillen's algebraic K-theory.

I will talk about joint work with B Calmès, Y Harpaz, F Hebestreit, M Land, K Moi, D Nardin, T Nikolaus and W Steimle, where we extend this construction to stable infinity categories equipped with a suitable quadratic functor, which encodes a formal notion of forms on the objects of the category.

This general framework allows us to establish a general relationship between Grothendieck-Witt theory and Ranicki-Wall's L-theory generalising a theorem of Schlichting, and to reprove and improve some classical results on the Grothendieck-Witt spectrum of rings.

Ian Leary (Southampton)
Contractibility of acyclic 2-complexes

There is no algorithm to decide which finite 2-complexes are simply-connected. On the other hand, the existence of an algorithm to decide which finite 2-complexes are contractible is a well-known open problem. I will discuss these questions and solve an analogous question for infinite complexes.