PhD defence, Thursday 16 January 2020. Erica Minuz.

2020.01.16 |

We describe a type of configuration space where some points are allowed to coincide. This can be encoded in a graph where the vertices correspond to the points in the configuration space and the edges record which of them are not allowed to overlap. In particular, we examine its cohomology through graph complexes. One of those is the graph complex defined by Baranowsky and Sazdanovic that is the first page of a spectral sequence converging to the homology of this type of configuration space. We compare it with the graph complex defined by Kontsevich and with the CDGA befind by Kriz and Totaro that is a rational model for the configuration space. Moreover, we establish a connection to the CDGA defined by Lambrechts and Stanley, that Idrissi proves to be a real model for the configuration space. We describe the cohomology of the configuration space dependent on a graph of points in the real space. Finally we define a version of little disks operad in the setting of this generalised configuration space.

The PhD degree was completed at the Department of Mathematics, Faculty of Natural Sciences, Aarhus University.

This résumé was prepared by the PhD student.

**Time:** Thursday 16^{ }January 2020 at 13:15-15:15

**Place:** Aud. G1 (1532-116), Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus C.

**Title of PhD thesis: **Graph complexes and cohomology of configuration spaces

**Contact information:** Erica Minuz, minuz@math.au.dk.

**Members of the assessment committee:**

Professor Najib Idrissi, Department of Mathematics, University of Paris, France

Professor Søren Galatius, Department of Mathematics, University of Copenhagen, Denmark

Professor Andreas Basse-O'Connor (chair), Department of Mathematics Aarhus University

**Main supervisor: **Professor Marcel Bökstedt, Aarhus University

The defence is public.

The PhD thesis is available for reading at the Graduate School of Science and Technology/GSST, Ny Munkegade 120, building 1521, 8000 Aarhus C.

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