Daniel Chan University of New South Wales Noncommutative surface singularities Friday 29th October, 12:05-12:55pm, Carslaw 175. Orders are examples of noncommutative rings for which many of the techniques of algebraic geometry can be used to study them. In this talk, I will give a leisurely introduction to some of the basic theory of orders. I will then look at some orders which are noncommutative analogues of quotient surface singularities. In the commutative case, there is a rich theory associated to these, and it seems that a similar picture is forming in the noncommutative case for orders. Our point of departure is the geometric notion of discrepancy which has come into vogue with the advent of Mori theory. This is quite different from other approaches via algebraic properties of quotient singularities. If time permits, applications to algebraic geometry will be given. This is joint work with Colin Ingalls and Paul Hacking.