Consider a Noetherian local ring (R, m) and an m-primary ideal a. The multiplicity of the ideal measures how fast the length of R/a^{n} grows. The notion of multiplicity extends similarly to the case when there are several m-primary ideals. It turns out that these mixed multiplicities have good convexity properties and I will sketch what these properties are.

The talk will mainly consist of three parts.
1) Definition of mixed multiplicities.
2) Relation with intersection forms.
3) Log concavity properties of mixed multiplicity. Speaker(s): Hyunsuk Kim (University of Michigan, Ann Arbor)