ERC Project: Resonances

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)

Preprints

1. How many inflections are there in the Lyapunov spectrum? (with O.Jenkinson and P.Vytnova)
2. Comparison theorems for closed geodesics on negatively curved surfaces (with S. Cantrell)
3. Uniform lower bounds on the dimension of Bernoulli convolutions (with V.Kleptsyn and P.Vytnova)
4. Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups (with P.Vytnova)
5. An infinite interval version of the alpha-Kakutani equidistribution problem (with B. Sewell)
6. Maximizing measures for Bernoulli measures and the Gauss map to appear in Proceedings of the American Mathematical Society.
   
7. Fourier multipliers and transfer operators, to appear in Journal of Fractal Geometry
8. The Schottky-Klein prime function and counting functions for Fenchel double crosses, to appear in Monatshefte fur Mathematik

Surveys

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

Computer Programmes

1. 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
2. A mathematica notebook for calculating the dimension of limit sets for Bernoulli IFS coming from finitely many inverse branches for the Gauss map
3. 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)