Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting @ Bristol 2023
The thirteenth 1-day meeting in additive combinatorics and analytic number theory will take place at the University of Bristol on
Thursday, 30th March 2023.
The series is funded by an LMS Scheme 3 Grant (31623).
Programme | Registration | How to get here | Participants | Bristol 2014 | Oxford 2015 | Bristol 2015 | Oxford 2016 | Imperial 2016 | Warwick 2017 | Bristol 2018 | Oxford 2018 | Cambridge 2019 | Oxford 2019 | Oxford 2022 | KCL 2022
Programme
10:45-11.00 Arrival
11:00-11.05 Welcome
11:05-11:45 Han Yu (Warwick)
Arithmetic properties of missing-digit numbers
| Abstract: | For an integer b>2, consider the set C of real numbers whose base b expansions have only digits in a certain set of digits. This C is a nice fractal set and is well-studied in Geometric Measure Theory. In this talk, we will explore some problems concerning some arithmetic properties of C, e.g. the sumset C+C, quotient set C/C, and product set C*C. In addition, we will also discuss some recent results on Diophantine Approximation on C. Part of this talk is based on joint work with Demi Allen (Exeter) Sam Chow (Warwick) and Peter Varju (Cambridge).
|
The structure of large sum-free sets in F_p^n
| Abstract: | A set A of F_p^n is sum-free if the sumset A+A does not intersect A. If p is congruent to 2 mod 3, it is known that the maximal size of a sum-free set in F_p^n is (p^n+p^{n-1})/3, and that for any sum-free set A in F_p^n of this size, there exists an (n-1)-dimensional subspace V such that A is the union of (p+1)/3 cosets of V. In this talk, we discuss the structure of sum-free sets that are slightly smaller than (p^n+p^{n-1})/3. For the special case p=5, we will sketch a proof of the fact that any sum-free set A in F_p^n of size larger than 1.2 x 5^{n-1} is contained in two cosets of an (n-1)-dimensional subspace.
|
14:30-15:10 Maria-Romina Ivan (Cambridge)
Monochromatic sums and products over the rationals
| Abstract: | Hindman's Theorem states that whenever the natural numbers are finitely coloured there exists an infinite sequence all of whose finite sums are the same colour. By considering just powers of 2, this immediately implies the corresponding result for products: whenever the naturals are finitely coloured there exists a sequence all of whose products are the same colour.
But what happens if we ask for both the sums and the products to all have the same colour? It turns out that this is not true: it has been known since the 1970s that there is a finite colouring of the naturals for which no infinite sequence has the set of all of its sums and products monochromatic.
In this talk we will investigate what happens to this question if we move from the naturals to a larger space such as the dyadic rationals, the rationals, or even the reals. Joint work with Neil Hindman and Imre Leader.
|
The asymmetric additive energy of polynomials
| Abstract: | In this talk we will see how sieve techniques can be used to count the number of solutions to certain Diophantine equations and in particular prove that polynomials have small "asymmetric additive energy."
|
16:30-17:10 Julia Stadlmann (Oxford)
Mean square gap between primes
| Abstract: | Given a fixed real number a>0, for how many choices of x does the interval [x,x+x^a] contain primes? If X is large, the Riemann hypothesis suggests that [x,x+x^a] contains primes for all but O(X^(1-a) log(X)^3) choices of x in [X,2X] and, if a > 1/2, [x,x+x^a] contains primes for all x in [X,2X]. Weaker unconditional results are also known, but their strength decreases rapidly as a decreases - it is hard to count primes in short intervals.
In this talk we discuss how results from analytic number theory can be combined with combinatorial methods from sieve theory to prove and improve upper bounds on the number of short intervals not containing any primes. This also allows us to deduce upper bounds on the mean square gap between primes.
|
Sharp quantitative stability for the Brunn-Minkowski inequality
| Abstract: | The Brunn-Minkowski inequality states that for bounded open sets A and B in R^d, we have |A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}. Equality holds if and only if A and B are convex and homothetic sets in R^d. In this talk, we present sharp stability results for the Brunn-Minkowski inequality, answering a question of Figalli and Jerison.
|
All talks will take place in Room 2.41 in the Fry Building, School of Mathematics, University of Bristol.
If you would like to join us for dinner at Pizza on the Park from 18.30, please make sure you fill in the registration form below.
Registration
To register please fill in the registration form by Sunday, 26th March. It is particularly important that you let us know in advance, via the form, if you wish to join us for dinner. The participants list below will be updated accordingly, but this may take a few days.
How to get here
The meeting will take place in the School of Mathematics, Fry Building, Woodland Road, Bristol, BS8 1UG. The main entrance to the building is just downhill from the junction between Woodland Road and University Road.
Room 2.41 is on the second floor. On entering through the main entrance, walk ahead past the porters' desk until you come to the main staircase in the atrium. Climb all the way to the top floor, turn left into the corridor, and then 2.41 will be immediately on your left.
There are two train stations in Bristol. The most convenient for the university is Bristol Temple Meads, from where it is either a half-hour walk or a 15-minute taxi journey to the Fry Building. Alternatively, 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. Get off the bus at the Clifton triangle, the top of Park Street, opposite the Wills memorial tower. Timetables are available here.
Please remember that if you are hoping to claim reimbursement of your expenses through WOMBL, please book your tickets as far in advance as possible to keep costs down.
Important: The RMT union has announced a rail strike for 30th March, so do plan and monitor your travel arrangements accordingly. If you are planning to travel by car and are able to offer other participants a ride, you could share the information at http://www.groupcarpool.com/t/cwnk2h. (Please use responsibly: only offer a trip you firmly intend to make to others, and show up on time for any journey you've asked to share.)
Participants
Faustin Adiceam, Université Paris-Est Créteil
Daniel Altman, University of Oxford
Kirsti Biggs, Uppsala University
Jonathan Bober, University of Bristol
Jonathan, Chapman University of Bristol
Hou Tin Chau, University of Bristol
Jake Chinis, University of Bristol
Sam Chow, University of Warwick
David Ellis, University of Bristol
Merlin Haith Rowlatt, University of Bristol
*Ben Green, University of Oxford
Lasse Grimmelt, University of Oxford
Maria-Romina Ivan, University of Cambridge
Oliver McGrath, King's College London/Heilbronn Institute
Alexandru Pascadi, University of Oxford
Jonathan Passant, University of Bristol
Sarah Peluse, Princeton/IAS
*Sean Prendiville, Lancaster University
Steven Robertson, University of Manchester
Besfort Shala, University of Bristol
Ilya Shkredov, LIMS
Julia Stadlmann, University of Oxford
*Matthew Tointon, University of Bristol
Leo Versteegen, University of Cambridge
Jackie Voros, University of Bristol
*Aled Walker, King's College London
Fei Wei, University of Oxford
*Julia Wolf, University of Cambridge
Han Yu, University of Warwick
* Organisers