Splash Biography
JOE SHNYDER, Aspiring homotopy theorist
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Major: Mathematics College/Employer: Princeton Year of Graduation: 2025 |
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Brief Biographical Sketch:
My least favorite parts of mathematics are numbers, equations, and inequalities. Even if you use fancy Greek letters, or weird names like ``sin'' or ``log'', at the end of the day it's still a number. Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)M680: The Brouwer Fixed-Point Theorem: A Journey into Algebraic Topology in Splash 2023 (Apr. 22, 2023)
As L. E. J. Brouwer was stirring his coffee one day, he noticed one point seemed to remain motionless. Indeed, after stirring a cup of coffee, on bit of liquid must be in exactly the same place that it started in. This a result known as the Brouwer Fixed-Point Theorem, which I will prove in this class. Along the way, I will introduce some of the basic ideas of the beautiful subject known as Algebraic Topology, including the concepts of homotopy and the fundamental group.
M697: Abstract Nonsense (or rather, Category Theory) in Splash 2023 (Apr. 22, 2023)
Much of contemporary mathematics is indebted to techniques developed in the 1940s affectionately dubbed "abstract nonsense" by their practitioners, due to their great generality. However, despite the esoteric terminology and notation, these subjects such as category theory and homological algebra are extremely affable and gorgeous when one takes the time to befriend them; and have lead to the development of entirely new fields such as homotopy theory. In this course we will introduce the basic notions of categories, functors, and natural transformations through elementary examples; culminating with a proof of Yoneda's Lemma. The content will be based off of previous experiences teaching this subject at the high school level.
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