Rafael Sayous

I am interested in ergodic homogeneous dynamics and related applications to equidistribution problems (gaps, pair correlations) of families arising from number theory in a global (number or function) field.

Doctoral student supervised by Jouni Parkkonen (Jyväskylän Yliopisto) and Frédéric Paulin (Université Paris-Saclay) since September 2022.

Publications and preprints

Gaps in the complex Farey sequence of an imaginary quadratic field, July 2024, hal-04638605, arXiv:2407.04380.

Effective pair correlations of fractional powers of complex grid points, October 2023, to appear in Combinatorics and Number Theory, hal-04352084, arXiv:2310.19578.

Effective pair correlations of fractional powers of integers, June 2023, hal-04352082, arXiv:2306.00793.

Talks

Talk entitled Asymptotic of gaps in Gaussian fractions at the workshop Geometry, groups and dynamics, ENS Lyon (France), June 2024.

Talk entitled Equidistribution of divergent diagonal orbits in positive characteristics at the workshop Diagonal actions in the space of lattices (from counting problems to Diophantine approximation), École Polytechnique, Palaiseau (France), March 2024.

Talk entitled Pair correlations of fractional powers, two examples at the Analysis Seminar, Jyväskylän Yliopisto (Finland), December 2023.

Talk entitled Some number theoretical applications of ergodic theory, Seminar for Young Researchers, Jyväskylän Yliopisto (Finland), November 2023.

Conferences
and summer schools

Attendance to the conference entitled Group Actions with Hyperbolicity and Measure Rigidity, during the thematic trimester Group Actions and Rigidity: Around the Zimmer Program, Institut Henri Poincaré, Paris (France), May 2024.

Attendance to the Zurich Dynamics School and Conference, Universität Zürich, Zurich (Switzerland), June 2023.

Attendance to the summer school entitled Topics on the Geometry of Locally Symmetric Spaces, Universidad de la República, Montevideo (Uruguay), February-March 2023.

Side Projects

Location manager for the short movie Kipinä submitted to the Nikon Film Festival, February 2024.