# 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

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 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

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.