# ERC project: Resonances

## Participants

Coordinator: Mark Pollicott

PhD Students

- Daofei Zhang (2020-2024)
- Alexander Baumgartner (2020-2024)

Externally funded PhD students

- Ben Sewell (EPSRC)
- Paul Colognese (EPSRC)
- David Parmenter (Warwick University)

Postdoctoral Researchers

- Julia Slipantshuk (2021-2024)
- Jungwon Lee (2021-2024)

Externally funded Postdoctoral Researcher

- Polina Vytnova (EPSRC)

### Visitors

- Vadim Kaimanonovich
- Khadim War

### Scientific articles

- How many inflections are there in the Lyapunov spectrum? (with O.Jenkinson and P.Vytnova)
- Comparison theorems for closed geodesics on negatively curved surfaces (with S. Cantrell) to appear in
*Groups, Geometry and Dynamics* - Uniform lower bounds on the dimension of Bernoulli convolutions (with V.Kleptsyn and P.Vytnova), to appear in
*Advances in Mathematics* - Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups (with P.Vytnova) to appear in
*Transactions of the American Mathematical Society* - An infinite interval version of the alpha-Kakutani equidistribution problem
*(with B. Sewell)* - Maximizing measures for Bernoulli measures and the Gauss map to appear in
*Proceedings of the American Mathematical Society.* - Fourier multipliers and transfer operators, to appear in Journal of Fractal Geometry
- The Schottky-Klein prime function and counting functions for Fenchel double crosses, to appear in Monatshefte fur Mathematik
- Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra (with C. Matheus, C. Moreira and P. Vytnova)
- An upper bound on the dimension of the Rauzy gasket (with B. Sewell)
- Minimizing entropy for translation surfaces (with P. Colognese)
- Accurate bounds on Lyapunov exponents for expanding maps of the interval (with P. Vytnova)
- Maximizing measures for Bernoulli measures and the Gauss map to appear in
*Proceedings of the American Mathematical Society* *Zeta functions in higher Teichmuller theory (with R. Sharp)*

### Surveys

- A dynamical approach to validated numerics (survey: with O.Jenkinson)
- Statistical properties of the Rauzy-Veech-Zorich map (with R.Aimino), to appear in SLNM (JM volume)

### Computer Programmes

- An online programme to calculating the dimension of limit sets for IFS coming from finitely many inverse branches for the Gauss map and a Markovian condition
- A mathematica notebook for calculating the dimension of limit sets for Bernoulli IFS coming from finitely many inverse branches for the Gauss map
- A mathematica notebook for calculating the dimension of the Cantor set E2 (consisting of numbers whose continued fraction expansion uses only the digits 1 or 2)