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K-State Today

January 21, 2016

Mathematics Colloquium lecture Jan. 21

By Reta McDermott

Xiannan Li, University of Oxford, will present "Prime Numbers in Thin Polynomial Sequences" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Jan. 21, in 122 Cardwell Hall.

The abstract for the lecture is: A fundamental problem in analytic number theory is to prove that there are infinitely many primes in interesting sets. This goal has long been the dream of sieve theorists, and indeed, is the main motivation behind creation of sieve theory.

Unfortunately, there are fundamental difficulties involved in this pursuit. Around 15 years ago, there were breakthroughs due to Friedlander and Iwaniec, and Heath-Brown. Very recently, Heath-Brown and Li proved that there are infinitely many primes of the form $x^2 + p^4$ where $p$ is prime. Li will describe some of the ideas involved and give some taste of the myriad challenges in this area.

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