Ph.D. Defense Oscar Bendix Harr

Thesis title: Sheaves and moduli spaces of manifolds

This thesis examines two topics in the intersection between topology and geometry: sheaves and moduli spaces of manifolds. These themes are tied together by the fourth and last article included in the thesis. In this article, we prove a sheaf-theoretic enhancement of the family Stokes theorem using the six-functor formalism for sheaves on locally compact Hausdorff spaces. We apply this theorem to the study of moduli spaces of manifolds with a free boundary, producing new relations between generalized MMM and gravitational descendant classes. The remaining three articles in the thesis deal either with the cohomology of moduli spaces using non-sheaf-theoretic techniques and with properties of sheaf categories.

Thesis 

Supervisor: Professor Jesper Grodal (principal), University of Copenhagen:
Co-supervisor: Professor Nathalie Wahl, University of Copenhagen

Assessment committee:

Professor Henrik Holm (chair), University of Copenhagen
Professor Johannes Ebert, University of Münster
Associate Professor Achim Krause, University of Oslo