Computer Science Program and Mathematics Program Present

Do Circles Really Have Unique Centers? An Introduction to P-adic Numbers

We all have an intuitive notion of 'distance' between two numbers. For example, we might say that the distance between the numbers 3 and 5 is 2, and the distance between -5 and 1 is 6. But what do we really mean by 'distance'? Are there other ways to measure numbers? It turns out that the answer is yes: for every prime number p, there is a way to measure numbers in terms of their divisibility by p. In doing this, we are led to the world of "p-adic numbers", a strange place where all triangles are isosceles and where every point in a circle is its center. The theory of p-adic numbers permeates nearly all aspects of modern number theory. In this talk, we will define and gain intuition for the p-adic numbers and see some of their applications to problems in number theory.

Rylan completed his bachelor's degree in mathematics and music performance at Bard College, where he was also a cellist in the conservatory. He obtained a master's degree from the University of Cambridge, where he also performed with the Cambridge Philharmonic, and a PhD from UMass Amherst. Rylan currently teaches at Union College in Schenectady, New York. His research is in algebraic number theory and arithmetic geometry.

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For more information, call 845-758-6822, or e-mail [email protected].

Time: 12:00 pm – 1:00 pm EDT/GMT-4

Location: RKC 111

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