*Speaker:***Prof Martin Hyland ** (DPMMS*Venue: *Old Combination Room, Trinity College*Time: ***21/02/2011 20:30**, drinks from **20:15**

Algebras are vector spaces equipped with a multiplication (for example, the cross product in 3-space). Quadratic algebras are a special class of algebra with a duality theory involving the so-called dual numbers. The dual numbers give the algebra of differentiation. One can pass from algebras to suitable algebraic theories, called operads. There is a notion of a ‘quadratic operad’ with an analogous rich theory involving Lie algebras. Using examples, I shall try to explain some of this and its significance.