Drew Zemke

Ph.D. (2018) Cornell University

First Position

Preceptor in Mathematics, Harvard University

Dissertation

Surfaces in Three- and Four-Dimensional Topology

Advisor

Jason Manning

Abstract

Abstract: We investigate two ways in which a surface embedded or immersed in a manifold can reveal information about topology of the ambient space. In particular, we prove a special case of the Simple Loop Conjecture for 3-Manifolds and the study trisections of 4-manifolds from the perspectives of the mapping class group and the curve complex of a surface.