String Dualities and Geometry
Abstract: String theory has been physicists' most promising candidate thus far for a quantum theory of gravity. However, as of yet there have been no phenomenological consequences of the theory that can be tested by experiment. As such, many physicists view the theory more as "fancy mathematics" than a physical theory of reality. But unlike any other theory of physics which precedes it, dualities in string theory make highly non-trivial mathematical predictions motivated by the physical arguments of the theory, which strikingly enough turn out to be true in most cases. The motto seems to be that string dualities lead to unexpected links between different categories of geometry, which mathematicians may never have realized in isolation. So from a mathematical viewpoint, string theory is quite compelling to say the least. Regardless of whether or not string theory is indeed a physical theory of reality, thinking about the world in this way has greatly broadened the horizons of 21st century mathematics. So even if the theory is false, it has not been in vain. In this talk we will briefly explore the surface of the deep waters that are string dualities and their links with geometry from a non-technical standpoint.