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This week I am giving a talk at the Department of Mathematics and Systems Analysis of Aalto University where I will discuss results from a recent paper with Mihalis Kolountzakis. I will give a short introduction to different notions of … Continue reading
0. About these notes The notes that will follow are meant to be a companion to the Harmonic Analysis course that I’m giving this semester at IST. These notes are inspired, influenced and sometimes shamelessly copied from books, lecture notes … Continue reading
In this post I will try to give a description of an older result of mine that studies the operator norm of the maximal function along a polynomial curve. The relevant paper can be found here. The main object of … Continue reading
My coauthor George Costakis and I have recently uploaded to arxiv our paper “Szemerédi’s theorem, frequent hypercyclicity and multiple recurrence”. As I’m invited to talk about this subject next month, I will try to give here a general overview of … Continue reading
1. The set of squares does not contain arbitrarily long arithmetic progressions. As we have mentioned in the beginning of this discussion, Rudin was originally interested (among other things) in the number of terms the set of squares has in … Continue reading
This is the second post on Rudin’s conjecture. For the first introductory notes see here. In this post I will try to build some more intuition on sets by studying some examples and discussing their properties. We will also discuss … Continue reading
1. Introduction. This is the first of a series of posts concerning the RudinHardyLittlewood Conjecture. To give a taste of the problem right away let us consider to be a trigonometric polynomial of the form where for . The main … Continue reading