Gerhard Huisken was this year’s choice for the Britton Lectures – an annual series of talks given by a distinguished researcher working in the field of mathematics. Dr. Huisken’s topic this year had to do with measuring the mass of gravitational system (planets orbiting around each other, orbiting around a black hole, etc…).
It was pretty intense….
I will not try to summarize, mainly because I can’t, but I do think that the setting for this type of research is worth mentioning. For starters, the bulk of the research deals with how things flow along a given surface, and flows, or more generally vector fields, come up absolutely everywhere. Recall that a “flow” can be represented as a vector (something with magnitude and direction) associated to every point on a surface. Essentially this just means that if you are walking along a surface (could be curved, could be flat, could have holes, etc…), the flow tells you at every point where to go and how fast to get there. More complicated flows will have things called sinks and sources, otherwise known as singularities. Think of water draining out of your bathtub…
The really interesting thing is that the effect of a singularity can be described in terms of the geometry of the space that it is acting on. Take the bathtub example: you could describe the flow of water analytically by attaching to every point in the tub the direction and magnitude of the water flow, with some fairly complicated stuff happening at the drain, or you could imagine that the water is simply flowing quite naturally, but that the surface that it is flowing on looks something like this:
One of Huisken’s results is that if you were to replace the drain of your bathtub with a black hole, then the horizon of that black hole, i.e. the region of space from which no part of the flow can escape, is a minimal surface. Moreover, he proposed a method of actually finding this minimal surface. Which is pretty astounding.
So while I’m not totally sure how such relativistic inquiries translate into architectural objects, many of the techniques and resulting forms seem to at least suggest an application.
In any case, it was a fascinating talk by a leading researcher and a very good way to spend a Friday afternoon.