Janis Lazovskis, Department of Pure Mathematics, University of Waterloo
“Complex submanifolds”
Abstract: Complex submanifolds are defined similarly to their real counterparts, but there are some results that have absolutely no analogue in real-valued space. These involve conditions when the submanifold is compact and existence from any holomorphic function, the latter of which implies that an injective holomorphic map is biholomorphic. I will define complex submanifolds, give some basic properties, then prove and discuss the mentioned assertions and their consequences.