(1) Bivariate multifractal analysis (with C.Esser):
We study the exact bivariate multifractal spectrum of mappings in situation where these spectrum are supposingly independent. In particular we aim at proving or disproving a conjecture of Abry, Jaffard, Leonarduzzy, Seuret and Wendt regarding these spectrums made in 2018. A preprint will be available soon.
(2) Shrinking targets asscoiated with homogeneous self-similar IFS satisfying exponential separation:
In a previous preprint I established a formula regarding the dimension of shrinking targets associated with self-similar IFS for which the Hausdorff dimension and the similarity dimension agrees. In this project, we establish a more general formula which holds for sufficiently small shrinking targets associated with self-similar IFS with possible exact overlaps , similarity dimension possibly larger than the dimension of the ambiant space, satisfying the exponential separation condition. The preprint will be available soon, possibly this month.
(3) Rectangular Shrinking targets asscoiated with self-similar IFS (with D.Allen, T. Jordan, B. Ward, C. Wilson):
In a previous preprint work, Allen, Jordan and Ward and I independently studied the Hausdorff dimension of rectangular shrinking targets associated with missing-digit sets. We currently work together with Charlie Wilson, to generalize and extend theses results to various settings.