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What is this?
So many videos! I'm currently developing a series on topology, manifolds, and n-dimensional Euclidean space.
I have plans to explore many other topics in the future:
-The construction of the integers, rationals, and reals -- all beginning with the empty set.
-Zeno's paradox, convergence, and the topology of metric spaces.
-Polyhedra and their symmetries, groups and isomorphisms.
-Combinatorics, Pascal's triangle, and normal distributions.
-The geometry of the torus, including a higher production-value version of this video.
-Knot theory, Seifert surfaces, and the Arf invariant.
-Constructing and visualizing 3-manifolds.
Who are you?
Glad you asked! Hotel Infinity is a growing collection of videos exploring advanced math concepts through story-telling.
Current videos examine Hilbert's classic hotel paradox about the nature of infinity, the significance of irrational numbers, and an introduction to the field of topology. We have plans for many more videos in the future, exploring topology, abstract algebra, real analysis, and combinatorics.
What kind of math do you do?
I'm Tova Brown, nice to meet you! I earned my PhD in pure mathematics from MIT in 2011, and my bachelor's degree in math from UC Santa Cruz in 2006. I was an Assistant Adjunct Professor of mathematics at UCLA from 2011 until 2015.
I live by the sea with a little dog. I spend my spare time folding origami, drawing crazy shapes, and making math videos. Pictured: Me posing with a grapefruit for maximum color contrast.
Topology/geometry. Basically, I study crazy shapes that don't exist, it's pretty fun.
Here's the paper I wrote based on my PhD thesis, it has a bunch of nice pictures of the crazy shapes in question.