Additive Combinatorics @ Bristol 2014
We are pleased to announce that we will be holding a 1-day additive combinatorics meeting at Bristol on
|Arithmetic Removal lemmas and independent sets in hypergraphs
| In the last years, several authors have studied sparse and
analogues of a wide variety of results in extremal combinatorics. Very recently, due to the work of Balogh, Morris, and Samotij, and the work of Saxton and Thomason on the structure of independent sets on hypergraphs several of these questions have been addressed in a new framework by using the so-called containers in hypergraphs.
In this talk I will present how to use this technology together with Arithmetic Removal Lemmas due to Serra, Vena and Kral in the context of arithmetic combinatorics. We will show how to get sparse (and random) analogues of well known additive combinatorial results even in the non-abelian situation.
This talk is based on a work in progress joint with Oriol Serra and Lluis Vena.
12:00-12:45: Tom Sanders
|Open problems in sumsets
14:15-15:30: Thomas Bloom
|Structure in large spectra and applications to Roth's theorem
|Large spectra, sets of frequencies where the Fourier transform of a
set is particularly large, play an important role in many problems of arithmetic combinatorics. A important result about such sets is Chang's lemma, which gives a sharp bound for the additive dimension of such sets, the size of the largest dissociated subset. We present a new structural lemma which, for certain applications, gives a quantitative improvement of Chang's lemma. As an application, we discuss how this can be used to obtain a quantitative improvement of Roth's theorem on three term arithmetic progressions.
15:15-16:00: Mark Walters
|Fast wins in n-in-a-row games
|The n-in-a-row game is a Maker/Breaker game played on the points of
Each player takes it in turns to pick a point and Maker wins if he gets n consecutive points on a line with any slope. In the fast variant then rather than picking one point each turn each player picks t points on the t-th turn. Obviously maker can win this game by time n, but can he win any sooner? We answer this and give a much stronger result.
16:15-17:00: Julia Wolf
|Ramsey multiplicity of patterns in abelian groups
|The Burr-Rosta conjecture attempted to classify those small graphs H
for which the random 2-colouring of the edges of the complete graph K_n contains (asymptotically) the minimum number of monochromatic copies of H. It was disproved by Sidorenko, who showed that it was false when H is a triangle with a pendant edge. Despite a number of other special cases having been resolved since, the general classification problem remains wide open. We explore an analogous question concerning monochromatic additive configurations contained in 2-colourings of the cyclic group Z_p and the finite-dimensional vector space F_p^n. (This is joint work with Alex Saad.)
This meeting is open to all. There is no registration fee, but please help us plan by completing the registration form if you are planning to attend. Limited financial support is available to enable the participation of junior researchers. Applications for financial support from early-career researchers must be received by July 18th.
The main train station in Bristol is Bristol Temple Meads. You may check departure and arrival times on the National Rail website. Advance purchase of tickets is highly recommended.
Upon arriving at the train station you may take buses no. 8 or 9 in the direction of Clifton, leaving from the bay on the right just beyond the taxi rank. A single trip costs £1.50 (get off at Clifton triangle), and usually takes under 20 minutes. Timetables are available here. A taxi from the train station to the maths department normally costs under £10, and the trip should take less than 15 minutes.
For those coming from afar, Bristol has an international airport that is particularly well served by easyjet and KLM airlines. There is a bus from the airport to the train station.
There are a number of pleasant accommodation options within walking distance for those participants wishing to stay overnight. In order of ascending room rates these are
• Washington Guesthouse
• Clifton House
• The Rodney Hotel
• The Berkeley Square Hotel
If you are a speaker or have been granted financial support and have informed us that you require accommodation, then we will make a booking on your behalf. Otherwise we ask that you please contact the hotel directly to make your reservation, and mention that you are attending this conference to receive a university discount on the standard rate.
Participants will need to make their own arrangements for lunch. After the last talk there will be a cheese and wine reception on the veranda of the Main Maths Building, followed by a conference dinner at No. 4 Clifton Village.
The University of Bristol provides eduroam access. For those participants not already in possession of an institutional login we are able to issue a guest pass for the visitors' network on the day.
To find out what's on in Bristol, and what is worth seeing during your visit, see visitbristol.co.uk.
Pierre-Yves Bienvenu, University of Bristol
Thomas Bloom, University of Bristol
Tim Browning, University of Bristol
Sergiu Bursiuc, University of Bristol
Sam Chow, University of Bristol
Sean Eberhard, University of Oxford
Ben Green, University of Oxford
Karen Gunderson, University of Bristol
Omid Hatami, University of Cambridge
Bob Hough, University of Oxford
Oliver Johnson, University of Bristol
Tom Kealy, University of Bristol
Jakub Konieczny, University of Oxford
Zemer Kosloff, University of Warwick
Frederick Manners, University of Oxford
Justin McInroy, University of Bristol
Adam Morgan, University of Bristol
Rudi Mrazovic, University of Oxford
Sean Prendiville, University of Reading
Daniel Quiroz, London School of Economics
Luka Rimanic, University of Bristol
Edva Roditty-Gershon, University of Bristol
Misha Rudnev, University of Bristol
Juanjo Rué, Freie Universität Berlin
Alex Saad, University of Bristol
Tom Sanders, University of Oxford
Tony Skyner, University of Bristol
Jim Stankewicz, University of Bristol
Matthew Tointon, Université Paris-Sud (Orsay)
Aled Walker, University of Oxford
Mark Walters, Queen Mary University of London
Julia Wolf, University of Bristol
Trevor Wooley, University of Bristol