Derived A-infinity algebras

Sarah Whitehouse, University of Sheffield. Part of the algebra seminar series and algebra, geometry and integrable systems colloquium.

A-infinity algebras arise when one considers an operation which is associative up to homotopy. As soon as one does this, one is led to a rich structure with an infinite family of operations. These structures have their origins in topology and they have become important in many different areas of mathematics, including algebra, geometry and mathematical physics.

I will explain what they are and briefly survey some of the places they arise. Then I will motivate and discuss a recent generalisation, known as a derived A-infinity algebra. These are important when working over a commutative ground ring rather than a field. Results include some new descriptions of these structures and a hierarchy of different notions of equivalence.

After each talk at 4:15pm there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber. 

Sarah Whitehouse, University of Sheffield