Daniela Egas Santander Address Department of Mathematical Sciences Office 04.1.06 Universitetsparken 5 2100 København Ø Denmark Work phone +45 35320726 Email daniela[at]math.ku.dk

I am a PhD student at the Department of Mathematical Sciences since February 2011. I am part of the Topology group and the Center of Symmetry and Deformation. My scientific advisor is Nathalie Wahl.
Currently I am interested in mapping class groups. The mapping class group of a compact oriented surface is the group of homotopy classes of orientation preserving homeomorphisms of the surface with itself. This concept can be extended to oriented surfaces with boundary by considering the homotopy classes of self- homeomorphisms of the surface which fix the boundary pointwise. In a similar fashion one can extend this to punctured surfaces or to open closed cobordisms. Not much is known about the unstable (co)homology of these mapping class groups. I am interested in studying graph complexes that model this (co)homology and the relations between them. Currently I am working with the graph complex coming from fat graphs. These are graphs with a cyclic ordering of the vertices (which one can think of as the skeleton of a given surface) where the differential of a fat graph is set to be the sum of all the fat graphs obtained by collapsing all possible edges.