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Mathematics Colloquium

Tuesday, February 9, 2016
4:00pm to 5:00pm
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East Bridge 201 (Richard P. Feynman Lecture Hall)
Polynomials representing primes
James Maynard, Mathematical Institute, Magdalen College,

It is a famous conjecture that any one variable polynomial satisfying some simple conditions should take infinitely many prime values. Unfortunately, this isn't known in any case except for linear polynomials - the sparsity of values of higher degree polynomials causes substantial difficulties. If we look at polynomials in multiple variables, then there are a few polynomials known to represent infinitely many primes whilst still taking on `few' values; Friedlander-Iwaniec showed X^2+Y^4 is prime infinitely often, and Heath-Brown showed the same for X^3+2Y^3. We will describe recent work which gives a family of multivariate sparse polynomials all of which take infinitely many prime values. 

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