Applications of nilsequences to number theory
|
Thu, 10/02/2011 16:00 |
Ben Green (Cambridge) |
Number Theory Seminar  |
L3 |
| I will introduce the notion of a nilsequence, which is a kind of "higher" analogue of the exponentials used in classical Fourier analysis. I will summarise the current state of our understanding of these objects. Then I will discuss a variety of applications: to solving linear equations in primes (joint with T. Tao), to a version of Waring's problem for so-called generalised polynomials (joint with V. Neale and Trevor Wooley) and to solving certain pairs of diagonal quadratic equations in eight variables (joint work with L. Matthiesen). Some of the work to be described is a little preliminary! | |||