Facultad de Ciencias

Nilspaces, Gowers norms, and a generalization of the Green-Tao-Ziegler inverse theorem

Organiza

Departamento de Matemáticas

Ponente

Pablo Candela

Fecha

01-03-2019

Hora

11:30

Lugar

Módulo 17 - Aula 520 (Depto. Matemáticas UAM)

Observaciones

Pablo Candela
Universidad Autónoma de Madrid
 

Nilspaces, Gowers norms, and a
generalization of the Green-Tao-Ziegler
inverse theorem

 

Resumen:
The uniformity norms, introduced by Gowers in his famous work on Szemer´ edi’s theorem, have become a central tool in arithmetic combinatorics, especially to count linear configurations in subsets of compact abelian groups, and more generally to analyze averages of functions over such configurations. An important result related to the Gowers norms is the so-called inverse theorem, proved for functions on finite intervals of integers by Green, Tao and Ziegler. This theorem tells us essentially that such a function has large Gowers norm of order k+1 only if the function correlates with a specific type of function, called a nilsequence, that is generated by a rotation on a nilmanifold of step k. I shall discuss recent joint work with Bal ´ azs Szegedy in which, building up on the theory of nilspaces initiated by Camarena and Szegedy, we obtain in particular a generalization of the Green-Tao-Ziegler inverse theorem, valid for functions on compact abelian groups and also on nilmanifolds