# Seminars in geometry/topology

## Spring 2012

## Thursday May 3, 13:15 - 15:00, room 656, Sentralbygg 2

Sarah Whitehouse (University of Sheffield): *Derived A-infinity algebras from the point of view of operads*

**Abstract:** A-infinity algebras arise whenever one has a multiplication which is "associative up to homotopy". There is an important theory of minimal models which involves studying differential graded
algebras via A-infinity structures on their homology algebras. However, this only works well over a ground field. Recently Sagave introduced the notion of a derived A-infinity algebra in order to
extend the theory of minimal models to a general ground ring.

Operads provide a very nice way of saying what A-infinity algebras are - they are described by a kind of free resolution of a strictly associative structure. I will explain the analogous result for derived A_infinity algebras - these are obtained in the same manner from a strictly associative structure with an extra differential.

This is joint work with Muriel Livernet and Constanze Roitzheim.

## Monday March 26, 13:15 - 15:00, room 656, Sentralbygg 2

Richard Williamson: *Towards geometric hyperstructures*

**Abstract:** The notion of a 'hyperstructure', due to Nils Baas, can be viewed as a radical generalisation of a (higher) category. Rather than arrows between objects, 2-arrows between arrows, …, we allow very general 'bonds' between (possibly many) objects, 'bonds between bonds', … .

Manifolds, stratified by dimension, should assemble into a 'geometric hyperstructure', the bonds being glueings together of submanifolds.

I will discuss work in progress which aims to capture the rich combinatorics of this hyperstructure via opetope-like gadgets.

## Monday March 12, 13:15 - 15:00, room 656, Sentralbygg 2

Idun Reiten:*Cluster algebras and categories for topologists*

## Monday February 20, 13:15 - 15:00, room 656, Sentralbygg 2

Richard Williamson (University of Oxford and NTNU):*An introduction to higher order categories*

This is a continuation of the talk on Monday February 13.

## Monday February 13, 13:15 - 15:00, room 656, Sentralbygg 2

Richard Williamson (University of Oxford and NTNU):*An introduction to higher order categories*

This is a continuation of the talk on Monday January 30.

## Monday February 6, 13:00 - 14:00, Auditorium F6, Gamle fysikk

Marius Thaule:*The axioms for n-angulated categories*

**Abstract:** We will discuss the axioms for an n-angulated category, recently introduced by Geiss, Keller and Oppermann. In particular, we introduce a higher "octahedral axiom," and show that it is equivalent to the mapping cone axiom for an n-angulated category. For a triangulated category, the mapping cone axiom, our octahedral axiom and the classical octahedral axiom are all equivalent.

This is joint work with Petter Andreas Bergh.

## Monday January 30, 13:15 - 15:00, room 656, Sentralbygg 2

Richard Williamson (University of Oxford and NTNU):*An introduction to higher order categories*

This is a continuation from last week's talk. Notes are available here.

## Monday January 23, 13:15 - 15:00, room 656, Sentralbygg 2

Richard Williamson (University of Oxford and NTNU):*An introduction to higher categories*

**Abstract:** Higher categories are rich gadgets which arise in many different guises. The aim of this talk is to convey something of the essence of the notion, rather than to explain in detail any particular models - we will look at examples of higher categorical phenomena which arise in a concrete way in topology, algebra, and elsewhere, and which illustrate some guiding principles of higher category theory. Pre-requisites will be kept to a minimum!

Notes are available here.