Joel Moreira

Ergodic theorem involving additive and multiplicative groups of a field {x + y, xy} and patterns

We establish a ‘diagonal’ ergodic theorem involving the additive and multiplicative groups of a countable field

Derandomizing Restricted Isometries via the Legendre Symbol

K

New polynomial and multidimensional extensions of classical partition results

and, with the help of a new variant of Furstenberg’s correspondence principle, prove that any ‘large’ set in

Large subsets of discrete hypersurfaces in Z d contain arbitrarily many collinear points

K

Measure preserving actions of affine semigroups and \{x+y,xy\} patterns

contains many configurations of the form

A Conditional Construction of Restricted Isometries

\{x+y,xy\}

Van der Corput’s difference theorem: some modern developments

. We also show that for any finite coloring of

Optimal lower bounds for multiple recurrence.

K

A proof of the Erd\H{o}s sumset conjecture

there are many

A proof of the Erdős sumset conjecture

x,y\in K