Caltech Home > PMA Home > Calendar > Mathematics Colloquium
Tuesday, February 09, 2016
4:00 PM - 5:00 PM
East Bridge 201 (Richard P. Feynman Lecture Hall)

# Mathematics Colloquium

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.