# Homology of partition posets and Koszul duality of operads

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

**Speaker:** Benoit Fresse, University of Lille 1

**Abstract:** I consider partitions of a set with r elements {1...r}. This set forms a poset, with the order relation given by the refinement of partitions.
Let K(r) be the simplicial complex formed by chains of partitions which starts at the smallest element and ends at the largest element of this poset. The goal of this talk is to give a conceptual proof, in terms of a Koszul duality result for operads, that the cohomology of this poset K(r) is identified with the Lie representation of the symmetric groups in degree r-1, and vanishes otherwise.
I will relate partition posets to tree complexes, and I will use this picture to give an intuitive introduction to this application of the theory of operads.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 01/15/2013

**Time:** 2:30pm - 3:30pm