On Prime Numbers and Arithmetic Progressions
Professor Alan Taylor
January 12, 2015
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 4:45pm
The number-theoretic study of the interplay between prime numbers and arithmetic progressions goes back to some early work of Lagrange and Waring in the 18th century. Questions that have since arisen include the following:
The answer to the first (Dirichlet’s theorem) is one of the deepest results of the 19th century. The answer to the second (the Green-Tao theorem) is one of the deepest results of the 21st century. We’ll discuss these along with the original theorem (and proof) of Lagrange and Waring.
- Does every long arithmetic progression contain a large set of primes?
- Does every large set of primes contain a long arithmetic progression?
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