An undergraduate seminar during the fall of 2020.
I can introduce this topic no better than the excerpt on the primary text itself:
Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl.
This seminar is then a meander through the brilliant hyperbolic world of Felix Klein. With the aid of our computers, we will be able to marvel at the mise en abyme of Indra’s Pearls.
Curiousity and excitement are basically the only requirements for this seminar; mathematical notions will be discussed as they come up. Programming experience is helpful but not essential: it will simply make our journey so much more panoramic!
Beyond the mathematical content, I hope that the seminar will convey a sense of how mathematical research is conducted via play and experimentation, and also a feeling for how mathematics is communicated. I hope that the seminar will be very interactive, with lots of participation from both speaker and audience.
The primary reference for this seminar is the delightful
You can find a helpful, though technical, review of this book in the Notices of the American Mathematical Society from January of 2003, here:
Another book from which we may extract some more advanced topics is
We meet online Fridays between 12:00 PM and 2:00 PM, New York time. Mostly, there will be a first and second speaker, each speaking for approximately an hour.
