Winter 2019 Schedule
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1000 Ways to Die in Hyperbolic Space
Steve Trettel | January 30
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The surface of the earth is curved, a fact one can notice intrinsically by taking a friend to the equator and both walking straight north: initially you two begin your journey walking parallel to one another, but eventually collide at the north pole. Mathematically speaking, the positive curvature of the earth causes the straight line (geodesic) paths you two are walking on to converge. While harder to visualize, curvature is an important property of 3-dimensional spaces as well, and gaining intuition about curved 3-dimensional worlds leads to some fun mathematical thought experiments!
This talk will introduce 3-dimensional hyperbolic space, a negatively curved world (where initially parallel straight lines tend to diverge from one another) through reimagining some aspects of daily life when geometry acts in this new and surprising way. In particular, we will focus on some of the perils of visiting such a world for beings like us accustomed to flat space (spoiler alert: lots of seemingly innocuous activities such as riding on a train or trying the Ferris wheel at a carnival prove to be fatal!)
Zonotopal Tilings
Nic Brody | February 13
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I will describe how a piece of recreational mathematics can be viewed with an algebraic, combinatorial, geometric, or topological lens, and how it illustrates familiar theorems in each of these contexts. We’ll understand certain aspects of fiber polytopes, factorizing permutations, Reidemeister moves, Greendlinger’s lemma, and the Gauss-Bonnet theorem, all in the context of a (very easy) jigsaw puzzle.