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

Special Year Research Seminar

May 30, 2023 | 2:00pm - 3:00pm

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...

Special Year Research Seminar

May 16, 2023 | 2:00pm - 3:00pm

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...

Special Year Research Seminar

May 09, 2023 | 2:00pm - 3:00pm

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...

Special Year Research Seminar

May 02, 2023 | 2:00pm - 3:00pm

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.

Special Year Learning Seminar

April 19, 2023 | 10:30am - 12:00pm

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...

Special Year Research Seminar

April 18, 2023 | 2:00pm - 3:00pm

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...

Special Year Research Seminar

April 11, 2023 | 3:30pm - 4:30pm

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...

Special Year Research Seminar

April 04, 2023 | 2:00pm - 3:00pm

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...