Pure Maths Colloquium: Algebraic structures up to homotopy
28 November 2016 16:00 in CM221
Many familiar algebraic operations are associative. To a topologist, it is more natural to consider operations which are "associative up to homotopy" and I will discuss what this means. As soon as one does this, one is led to a rich structure with an infinite family of operations, known as an A-infinity structure. These structures have become important in many different areas of mathematics, including algebra, geometry and mathematical physics. One can play similar topological games with other algebraic conditions. I will survey some of this 50 year old story and discuss some recent developments.
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