Title of the talk: "Hausdorff dimension of self-similar measures and sets with common fixed point structure"

Date , Time & Venue : 08 Oct 2025  at 05:00 PM on Dept. of Mathematics

Abstract: In this talk, I will discuss the dimension theory of self-similar measures and sets on the real line, where the generating iterated function system (IFS) consists of some maps that share the same fixed point. These IFS have exact overlaps due to the common fixed-point structure. In this exact overlapping situation, the dimension theory becomes significantly more complicated. We determine a formula for the Hausdorff dimension of the self-similar measures and sets out of a Hausdorff co-dimension one exceptional set of natural parameters. This work significantly strengthens the previous result on dimension theory. As an application, we give the Hausdorff dimension of self-affine measures supported on the generalised 4-corner set. This is joint work with Prof. Balázs Bárány.  

About the Speaker: Dr. Manuj Verma completed his M.Sc. in Mathematics in 2018 from B.H.U. He earned his Ph.D. in January 2024 from I.I.T. Delhi.  Following his doctoral studies, he worked as an Early-Doc Fellow at IIT Delhi (January–March 2024). He recently finished a one-year post-doctorate from the Budapest University of Technology and Economics, Hungary, under the mentorship of Prof. Balázs Bárány. His research interests lie in fractal geometry, with a focus on the dimension theory of invariant sets and measures, the analysis of fractals, and applications of fractal geometry.