Abstract: The works of Furstenberg and Bergelson-Leibman on the
Szemeredi theorem and its polynomial extension motivated the study
of the limiting behavior of multiple ergodic averages of commuting
transformations with polynomial iterates. Following...
Abstract: I will present results establishing cancellation in
short sums of arithmetic functions (in particular the von Mangoldt
and divisor functions) twisted by polynomial exponential phases, or
more general nilsequence phases. These results imply...
Abstract: Abstract: We will discuss multilinear variants of
Weyl's inequality for the exponential sums arising in pointwise
convergence problems related to the Furstenberg-Bergelson-Leibman
conjecture. We will also illustrate how to use the...
Abstract: In this talk we present a natural generalization of a
sumset conjecture of Erdos to higher orders, asserting that every
subset of the integers with positive density contains a sumset
$B_1+\ldots +B_k$ where $B_1, \ldots , B_k$ are infinite...
ABSTRACT: In the 1970’s Erdos asked several questions about what
kind of infinite structures can be found in every set of natural
numbers with positive density. In recent joint work with Kra,
Richter and Robertson we proved that every such set A can...
Abstract: Given a fractal set E in $R^n$ and a set F in
$Gr(k,n)$, can we find k-plane S in F such that the orthogonal
projection of E onto S is large?
We will survey some
classical and recent projection theorems and discuss
their applications. ...
Abstract: For a topological dynamical systems (T, X) and a fixed
$x \in X$ we are interested in the distribution of prime and
semi-prime orbits, i.e. ${T px}p='$ and ${T p1p2 x}p1,p2='$. We are
interested in systems for which the related sequences...
Abstract: Given $B \subset N$, we consider the corresponding set
$FB$ of $B$-free integers, i.e. $n \inFB i_ no b \in B$ divides $n$. We
$de_{ne} X \eta_}$ the B-free subshift _ as the smallest
subshift containing $\eta := 1FB
\in {0, 1}Z$. Such...
Abstract: A central question in additive combinatorics is to
determine what class of structured functions is enough to determine
multilinear averages such as
