Ruzsa asked whether there exist Fourier-uniform subsets of ℤ/Nℤ
with very few 4-term arithmetic progressions (4-AP). The standard
pedagogical example of a Fourier uniform set with a "wrong" density
of 4-APs actually has 4-AP density much higher than...
I will discuss pointwise ergodic theory as it developed out of
Bourgain's work in the 80s, leading up to my work with Mirek and
Tao on bilinear ergodic averages.
In 1996 Manjul Barghava introduced a notion of P-orderings for
arbitrary sets S of a Dedekind domain, with respect to a prime
ideal P, which defined associated invariants called P-sequences. He
combined these invariants to define generalized...
In its dynamical formulation, the Furstenberg—Sárközy theorem
states that for any invertible measure-preserving system (X,μ,T),
any set A⊆X with μ(A) greater than 0, and any integer polynomial P
with P(0)=0,
The goal of this talk is to present new results dealing with the
asymptotic joint independence properties of commuting strongly
mixing transformations along polynomials. These results form
natural strongly mixing counterparts to various weakly and...
Erdős-style geometry is concerned with combinatorial questions
about simple geometric objects, such as counting incidences between
finite sets of points, lines, etc. These questions can be typically
viewed as asking for the possible number of...
Given n∈ℕ and ξ∈ℝ, let τ(n;ξ)=∑d|ndiξ. Hall and Tenenbaum asked
in their book \textit{Divisors} what is the value of
maxξ∈[1,2]|τ(n;ξ)| for a ``typical'' integer n. I will present work
in progress, carried out in collaboration with Louis-Pierre...
Complex dynamics explores the evolution of points under
iteration of functions of complex variables. In this talk I will
introduce into the context of complex dynamics, a new approximation
tool allowing us to construct new examples of entire...
The Mackey-Zimmer representation theorem is a key structural
result from ergodic theory: Every compact extension between ergodic
measure-preserving systems can be written as a skew-product by a
homogeneous space of a compact group. This is used, e.g...
