Geometry working seminar

Talk 1. Ningyan Wang, Pure Mathematics Department, University of Waterloo

“The K ̈ahler form on submanifolds of Rn + iRn”

I will discuss the restriction of the K ̈ahler form on Cn to submanifolds. A proof of Wirtinger’s inequality will be given, and its implications as a generalized Cauchy Riemann equation on submanifolds calibrated by the K ̈ahler form will be discussed. Its relation with Lagrangian manifolds will also be covered.

Talk 2. Justin Shaw, Pure Mathematics Department, University of Waterloo

“Introductory algebraic topology: The fundamental group”

We discuss path homotopy and why the fundamental group at a point is well defined. We then show that the fundamental groups of path connected points are isomorphic. This will allow us to define a simply connected space rigorously. If there is time we will compute the fundamental group of the circle or discuss higher homotopy groups. This talk is suitable for those who have taken a course in real analysis or point set topology and a course in differential geometry, but have taken no algebraic topology whatsoever.