Wenbo Sun

Multiple recurrence and convergence for certain averages along shifted primes

We show that any subset

A structure theorem for multiplicative functions over the Gaussian integers and applications

A\subset \mathbb{N}

Equidistribution of dilated curves on nilmanifolds: EQUIDISTRIBUTION OF DILATED CURVES

with positive upper Banach density contains the pattern

Dynamical cubes and a criteria for systems having product extensions

\{m,m+[n{\it\alpha}],\dots ,m+k[n{\it\alpha}]\}

A pointwise cubic average for two commuting transformations

, for some

Pointwise multiple averages for systems with two commuting transformations

m\in \mathbb{N}

Pointwise convergence of some multiple ergodic averages

and

Optimal lower bounds for multiple recurrence.

n=p-1

Quantitative multiple recurrence for two and three transformations

for some prime

Equidistribution of dilated curves on nilmanifolds

p