Category Archives: seminar notes

Circle discrepancy for checkerboard measures

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

Posted in math.CA, math.NT, open problem, paper, seminar notes | Tagged , , , , | Leave a comment

DMat0101, Notes 1: Quick review of measure theory

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

Posted in Dmat0101 - Harmonic Analysis, math.CA, Mathematics, seminar notes, Teaching | Tagged , , , , , , , | 1 Comment

The maximal function along a polynomial curve; effective dimension bounds.

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

Posted in math.CA, Mathematics, open problem, paper, seminar notes | Tagged , , , , , , | Leave a comment

Szemerédi’s theorem, frequent hypercyclicity and multiple recurrence

My co-author 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

Posted in math.DS, math.FA, Mathematics, open problem, paper, seminar notes | Tagged , , , , , | Leave a comment

The Rudin (Hardy-Littlewood) Conjecture, Notes 3: Omissions.

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

Posted in math.CA, math.CO, math.NT, Mathematics, open problem, seminar notes, The Rudin (Hardy-Littlewood) Conjecture | Tagged , , , , | Leave a comment

The Rudin (Hardy-Littlewood) Conjecture, Notes 2: A closer look at Λ(p)-sets.

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

Posted in math.CA, math.CO, math.NT, Mathematics, open problem, seminar notes, The Rudin (Hardy-Littlewood) Conjecture | Tagged , , , , | 7 Comments

The Rudin (Hardy-Littlewood) Conjecture, Notes 1: Introduction and basic facts.

1. Introduction. This is the first of a series of posts concerning the Rudin-Hardy-Littlewood 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

Posted in math.CA, math.CO, math.NT, Mathematics, open problem, seminar notes, The Rudin (Hardy-Littlewood) Conjecture | Tagged , , , , | 3 Comments