SMS scnews item created by Alex Casella at Tue 30 Aug 2016 1127
Type: Seminar
Distribution: World
Expiry: 29 Nov 2016
Calendar1: 5 Sep 2016 1700-1800
CalLoc1: Carslaw 535A
CalTitle1: MaPSS Seminar
Auth: casella@10.17.32.200 (acas5565) in SMS-WASM

MaPSS: Mathematical Postgraduate Seminar Series: Kamil Bulinski -- Equidistribution and Unique Ergodicity

Dear All,

We are delighted to present the MaPSS Seminar topic of Monday 29/08; please see the
abstract below.

**This Semester the Seminar will always run on Monday, at 5:00pm in 535A**

Following the talk, there will be pizza on offer.

Speaker: Kamil Bulinski (Sydney University)

Title: Equidistribution and Unique Ergodicity

Abstract: We all know that if  $\alpha \in \mathbb{R}/\mathbb{Z}$ is irrational, then
the sequence $\n \alpha$ is dense.  The goal of this talk is to prove that this is also
true for the sequence $n^2 \alpha$.  In fact, we will show that this sequence is
equidistributed (a result due to Weyl).  To do so, we will introduce some basic notions
in Dynamics and Ergodic Theory, culminating in a proof of Furstenberg’s result on the
unique ergodicity of skew products, which implies Weyl’s result.