Seminar

The functions we use in a calculus class are typically very well behaved.  So much so that we get used to not checking hypotheses before applying a theorem.   For instance, when using Taylor's Theorem, when was the last time you had to check that a function was $n$-times differentiable?  We usually work with the likes of $e^x$, $\cos x$, and $\sin x$, which can be differentiated over and over without ever stopping.  In fact, without googling, could you give an example of a function that can \textit{only} be differentiated \textbf{twice} at a point?

TBA

TBA

Abstract:

Self-dual vacuum spacetimes are known to be integrable following the work of Ted Newman and Roger Penrose. We will discuss the question of integrability in the case that the self-duality condition is dropped. 
 

Abstract:

After introducing the standard cross-ratio, we discuss a generalization of the cross-ratio to higher-dimensional Grassmannians. As an application, we give a short proof of the following theorem in projective geometry: Any four n-plane subspaces in general position in a projective space of dimension 2n+1 over an algebraically closed field have exactly n+1 common transversals.