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Special Year 2022-23: Dynamics, Additive Number Theory and Algebraic Geometry - Seminar

Let SO(3,R) be the 3D-rotation group equipped with the real-manifold topology and the normalized Haar measure \mu. Confirming a conjecture by Breuillard and Green, we show that if A is an open subset of SO(3,R) with sufficiently small measure, then...

This talk is based on a joint work with Steve Lester.

We review the Gauss circle problem, and Hardy's conjecture regarding the order of magnitude of the remainder term. It is attempted to rigorously formulate the folklore heuristics behind Hardy's...

Ruzsa asked whether there exist Fourier-uniform subsets of $\mathbb{Z}/N\mathbb{Z}$ 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...

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 1976, Gérard Rauzy proved a characterization of
deterministic numbers: y is deterministic iff for any normal
number x, x+y is also normal. During my lecture I will*
*discuss how normal and deterministic numbers behave under
arithmetic operations.* *I*...

In its dynamical formulation, the Furstenberg—Sárközy theorem
states that for any invertible measure-preserving system $(X, \mu,
T)$, any set $A \subseteq X$ with $\mu(A) > 0$, and any integer
polynomial $P$ with $P(0) = 0$,

$$c(A) = \lim_{N-M \to...

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...

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...