As part of the meeting we will celebrate the 30th anniversary of the network, which has been supported by the LMS since meetings began in 1996.
12:30 - 13:45 Lunch
14:00 - 15:00 Claire Burrin (Zurich)
15:00 - 15:45 Refreshments and Celebrations
15:45 - 16:45 Joel Moreira (Warwick)
17:00 - 18:00 Tuomas Sahlsten (Helsinki)
There will be a dinner afterwards.
Claire Burrin Rational points on the sphere
I will discuss recent developments concerning the distribution of rational points on the unit sphere, with connections to the covering radius problem and some number-theoretic problems.
Joel Moreira A structure theorem in topological recurrence
In 2005, Host and Kra developed a structure theory for general ergodic measure preserving systems which essentially allows one to reduce questions about multiple recurrence to a special class of systems of algebraic origin called nilsystems.
An analogous structure theory for minimal topological dynamical systems has since been slowly developing, with a recent breakthrough result by Glasner, Huang, Shao, Weiss and Ye describing a concrete relation with nilsystems. In this talk I will describe a recent work where we refine the GHSWY theorem in order to obtain applications for polynomial recurrence in minimal systems. This talk is based on joint work with Glasscock, Koutsogiannis, Le, Richter and Robertson.
Tuomas Sahlsten Quantum dispersion of (quasi)crystals via Fourier decay of dynamically defined measures
We show how the rate of quantum dispersion for many non-locally finite crystals and quasicrystals can be estimated through the Fourier decay of their spectral measures, which are typically dynamically defined. In the quasicrystal setting, these measures can arise from hyperbolic dynamics, for example through Axiom A diffeomorphisms on surfaces, as recently demonstrated in the groundbreaking work of Gaétan Leclerc on the Fibonacci Hamiltonian. In the case of non-locally finite crystals, the spectral measures may instead be generated by self-similar Weierstrass-type functions, which we report here. Both settings exhibit intrinsic nonlinearity that can be exploited using transfer-operator methods. This allows us to implement a Dolgopyat-type strategy adapted to low-regularity and non-smooth situations, where other recent advances to Fourier decay are not applicable. Joint work with Gaétan Leclerc (Helsinki) and Mostafa Sabri (Abu Dhabi).