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Washington State
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Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

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September 13, Monday, 4:10 - 5:00 PM

Jakob Streipel

Department of Mathematics and Statistics

Washington State University

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

Zoom

September 13, Monday, 4:10 - 5:00 PM

Jakob Streipel

Department of Mathematics and Statistics

Washington State University

Title: Diophantine approximation and counting
points on curves

Abstract: It is well known that we can approximate any real number arbitrarily well with rational numbers (the rationals are dense in the reals), but a much deeper and more interesting problem is trying to approximate real numbers well without using overly complicated rational numbers. E.g., 22/7 is a famously "good" rational approximation of pi, but what makes it "better" than, say, 3141/1000, which is much closer to pi?

In this talk we will explore and formalise some of these notions, use them to discuss fundamental properties of algebraic and transcendental numbers, and use some ideas from the proofs of these results to count special points on algebraic curves.

Abstract: It is well known that we can approximate any real number arbitrarily well with rational numbers (the rationals are dense in the reals), but a much deeper and more interesting problem is trying to approximate real numbers well without using overly complicated rational numbers. E.g., 22/7 is a famously "good" rational approximation of pi, but what makes it "better" than, say, 3141/1000, which is much closer to pi?

In this talk we will explore and formalise some of these notions, use them to discuss fundamental properties of algebraic and transcendental numbers, and use some ideas from the proofs of these results to count special points on algebraic curves.