OPEN NEIGHBORHOOD
October 6, 2021 4:30 pmIt is conjectured that there are infinitely many pairs of primes that differ by 2. After presenting some motivation, results toward the conjecture, and obstructions to further progress, we will...
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OPEN NEIGHBORHOOD
September 22, 2021 4:30 pmProjective space and complex tori are two of the simplest types of manifolds we encounter, and in many ways they seem very different from each other. I will try to...
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OPEN NEIGHBORHOOD
September 8, 2021 4:30 pmInteresting patterns of prime numbers can arise in recursively defined sequences (such as the Fibonacci sequence). For non-linear recursions, there are intriguing connections with complex dynamics and the Mandelbrot set....
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MATH TABLE, OPEN NEIGHBORHOOD
April 30, 2021 1:00 pmSpeaker: Kenz Kallal (Harvard) Title: The Arthur–Selberg trace formula and some applications to arithmetic statistics Speaker: Lux Zhao (Harvard) Title: The history and mathematics of the axiom of choice Go here to...
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OPEN NEIGHBORHOOD
April 21, 2021 4:30 pmIt is a classical fact that the product of a sum of two squares with a sum of two squares is naturally a sum of two squares. (One can also...
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OPEN NEIGHBORHOOD
April 7, 2021 4:30 pmI will talk, pretty casually, about random walks, which I first learned about as part of my Harvard undergrad thesis in finite group theory, and which turn out to be...
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OPEN NEIGHBORHOOD
March 17, 2021 4:30 pmThe periodicity of certain functions has been a topic of study throughout the long history of mathematics. It was a topic of study for you in high school trigonometry, and...
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OPEN NEIGHBORHOOD
March 3, 2021 4:30 pmAn evil mathematician has kidnapped the Harvard Pilgrim! To win his freedom, a group of undergrads must each find their name in a row of boxes. The odds look dire—but...
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OPEN NEIGHBORHOOD
February 17, 2021 4:30 pmWe will begin by discussing hyperbolic geometry, and how it can be used to build "evenly curved" metrics on a donut with one point removed. We will then discuss Maryam...
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OPEN NEIGHBORHOOD
February 3, 2021 4:30 pmWe will explore the idea of universality in probability theory, as seen in the central limit theorem, in which wide and varied input distributions can all give identical limiting outputs....
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