We are excited to be hosting an LMS One-Day Ergodic Theory Meeting at the University of Exeter on Wednesday 22nd October 2025. All the talks will be held in Amory C501 of the Amory building. We will also go for an evening meal (time and venue TBC) that all attendees are welcome to join us for. We would kindly ask that those intending to attend the meeting fill out the following form to give us an indication of numbers for ordering refreshments/arranging the evening meal:
If you have any questions, please do not hesitate to get in touch with either of the organisers Demi Allen (d.d.allen "at" exeter "dot" ac "dot" uk) or Charlie Wilson (cw1066 "at" exeter "dot" ac "dot" uk).
This meeting is part of the LMS Scheme 3 network of One-Day Ergodic Theory meetings between the University of Birmingham, the University of Bristol, Brunel University, Durham University, the University of Exeter, the University of Glasgow, Imperial College, Loughborough University, the University of Manchester, the Open University, Queen Mary, the University of St Andrews, the University of Surrey, UCL, and the University of Warwick. In addition, this meeting is funded in part by Demi Allen's LMS Emmy Noether Fellowship.
Schedule
12pm-1pm: Lunch
1pm-1.40pm: Nattalie Tamam (Imperial)
1.50pm-2.30pm: Manuel Hauke (Graz)
2.30pm-3pm: Coffee Break
3pm-3.40pm: Dorsa Vakilzadeh Hatefi (York)
3.50pm-4.30pm: Felipe Ramírez (Wesleyan)
Time TBC: Evening meal
Titles and Abstracts
Nattalie Tamam (Imperial)
Title: Weighted singular vectors for multiple weights
Abstract: It follows from the Dirichlet theorem that every vector has `good' rational approximations. Singular vectors are the ones for which the Dirichlet theorem can be infinitely improved. An (obvious) example of singular vectors are the ones lying on rational hyperplanes. We will discuss the existence of totally irrational weighted singular vectors on manifolds, and also ones with high weighted uniform exponent. We will also mention some invariance of weighted uniform exponents in the case of manifolds. The talk is based on a joint work with Shreyasi Datta.
Manuel Hauke (Graz)
Title: On twin primes, pseudo-random sequences and diophantine approximation
Abstract: In this talk, I will describe fine-scale statistics of sequences that typically arise in i.i.d. samples, and will discuss how to detect them in deterministic sequences such as $(a_n\alpha)_{n} \mod 1$ for integer sequences $(a_n)_n$ and irrational rotations $\alpha$. The focus will be on the sequence of primes and a generalization to so-called rough numbers. I will outline the proof strategy that includes a sieve coming from the twin prime counting problem, and establishing via random walks on Ostrowski digits an equidistribution result on diophantine Bohr sets mod d. This talk is based on https://arxiv.org/abs/2506.01736
Dorsa Vakilzadeh Hatefi (York)
Title: Hausdorff Dimension of Differences of Badly Approximable Sets
Abstract: The set of badly approximable numbers (real numbers with bounded continued fraction partial quotients), denoted by $\mathbf{Bad}$, has zero Lebesgue measure yet full Hausdorff dimension. In fact, it satisfies the stronger property of being a winning set in the sense of Schmidt’s game. The inhomogeneously badly approximable set, $\mathbf{Bad}^\gamma$, is also known to have full dimension. In this talk, we revisit these classical notions and proceed to prove that the set difference $\mathbf{Bad}^\gamma \setminus \mathbf{Bad}$ likewise has full dimension. Our proof relies on the dynamical interpretation of the problem on the space of unimodular grids and introduces a new variant of Schmidt’s game, the rapid game.
Felipe Ramírez (Wesleyan)
Title: Metric bootstraps for limsup sets
Abstract: In metric Diophantine approximation, we frequently encounter the problem of showing that a limsup set has positive or full measure. Often it is a set of points in $m$-dimensional Euclidean space, or a set of $n$-by-$m$ systems of linear forms, satisfying some approximation condition infinitely often. I will discuss results that allow us to bootstrap positive-measure statements from $m$-dimensional Euclidean space to the setting of $n$-by-$m$ systems of linear forms. This leads to proofs of the following form: Khintchine's theorem implies the Khintchine-Groshev theorem; the Duffin-Schaeffer conjecture implies the dual Duffin-Schaeffer conjecture; inhomogeneous Khintchine-type statements imply their linear forms analogues; and so on.
Travel
The meeting will happen at the main University of Exeter (Streatham) campus which is approximately a 20 minute walk from Exeter St Davids train station, albeit up a steep hill. Please note that there are two train stations in Exeter, Exeter Central and Exeter St Davids. Exeter St Davids is the main station, although it is about a 20 minute walk to campus from either.
Buses run from St Davids to the university on a fairly regular basis and there is also a taxi rank just outside the station. Specifically the Line 4 runs from the station to the University around every 15 minutes during peak times.
More details on travel can be found here.