This half-day workshop will look at recent research in Dynamical Systems. It is funded by an LMS Celebrating New Appointments grant.
The workshop will take place on the afternoon of Tuesday 1 July 2025 in the University of Manchester. Talks will take place from 13.30 to 16.30, followed by a reception and dinner. All are welcome to attend.
Contact: For queries and further details, please contact yotam.smilansky@manchester.ac.uk
Schedule
Talks are in Frank Adams 1, on the first floor of the Alan Turing Building.
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.
Title: Uniform distribution of saddle connection lengths
Abstract : Flat surfaces, examples of which arise from identifying opposite sides in a regular square or octagon, have interesting simple closed geodesics occurring in parallel families forming cylinders. It is of interest to count cylinders in terms of their circumference and ask finer distributional questions about their geometric properties. In this talk I will explain what that means and in particular discuss joint work with Jon Chaika and Benjamin Dozier on the uniform distributed mod 1 of the circumferences of such cylinders.
Title: Dynamics of hyperbolic tilings
Abstract : Substitution rules, well known for generating Euclidean aperiodic tilings, sequences of partitions and combinatorial words, can also be used to construct tilings of the hyperbolic upper-half space, which in turn provide a unifying framework for the study of these structures. In this talk, I will describe the construction and present results on the behaviour of hyperbolic tilings under horospheric and geodesic isometries, as well as on the associated dynamical zeta function. Based on ongoing work with Alon Nishry and Yaar Solomon.