Sometime in March of 2019, my colleague Howard Dierking asked me if I was interested in talking about my mathematical journey to a group of high school students. His wife Jennifer taught at the Bear Creek School in Redmond. She was looking to expose her kids to some outside perspectives on academia and research. She had a good reason for it - the students in her class were precocious. Rather than talk purely about my journey into Math, I thought I would mix relativity and geometry and throw in some fun facts about topology, gravitational waves, and GPS satellites. These were all topics that I was fascinated by. I was intrigued by the fact that an esoteric subject like General Relativity has a very practical application to location tracking via GPS satellites. Anyone who has used turn-by-turn directions on their smartphone knows the importance of accurately tracking one's location. Moreover, if you are in a plane that is landing using autopilot you know your life depends on the accuracy of those GPS satellites. But did you know that there are corrections that need to be made to the formulas to account for Special and General Relativistic effects? Time slows down when things travel fast such as the GPS satellites for instance. Time also goes faster the farther you are from the earth's gravitational field. For accurate triangulation of the location of a device, the devices on the GPS satellites will apply these relativistic corrections. Else your location will be subject to drift and you may end up very from where you need to be! To learn about some of these topics take a look at this slide presentation.
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