### Lorentzian geometry

According to the geometry of Einstein’s theory of gravity, a straight line can be perpendicular to itself, and the distance between a point and itself can be infinite! This is because concepts such as length, angle, distance, and curvature all depend, not just on the shape of the space you are studying, but also on the ruler and protractor you are using. Studying these shapes, together with the different kinds of “geometries” available on them, is one of my primary research interests.