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Advanced Talk: Using Symmetries to Solve Problems: An Introduction to Representation Theory

Abstract: Suppose that you have n kids sitting around a round table, each with a bowl of cereal in front of him/her. As soon as the teacher turns away, each kid steals half of the cereal of his neighbor to the right and half of the cereal of his neighbor to the left, putting it…Continue Reading Advanced Talk: Using Symmetries to Solve Problems: An Introduction to Representation Theory

Grad Student Talk: An Infinite Family of Triangles

Abstract: This will be a gentle discussion about my favorite theorem, Poncelet’s Porism. My goal is to provide intuition about the content of this theorem by focusing on a special case involving triangles. I’ll introduce spherical and hyperbolic geometry and discuss an application of the Porism in spaces of constant curvature. I will also explain…Continue Reading Grad Student Talk: An Infinite Family of Triangles

Faculty Talk: The Rationality of Irrationals

 Abstract: When I was in my freshman year at Stony Brook, a friend of mine was perplexed by an interesting question. Suppose we enumerate the rationals on the interval [0,1] in the “standard” way in which the denominators increase: 0, 1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6, 1/7, … Suppose…Continue Reading Faculty Talk: The Rationality of Irrationals