I am an instructor and research postdoc (“adiunkt”) at the Wroclaw University of Science and Technology (Politechnika Wrocławska). I recieved my Ph.D. in Mathematics from The Pennsylvania State University in 2018.
Research area
There is a classical connection between real "minus continued fractions"
\[ a_0 - \dfrac1{a_1 - \dfrac1{a_2 - \dfrac1{\ddots}}} \]
and geodesic flow on the modular surface $\mathrm{PSL}(2,\mathbb Z) \backslash {\mathcal H}^2$. This overlap of number theory, geometry, and dynamical systems has inspired much of my current research program, which essentially consists of three settings:
natural extensions and symbolic coding,
entropies ($h_{\mu}$ and $h_{\rm top}$) of piecewise monotone circle maps,
preservation and destruction of normality.
My individual published work focuses on Gauss-like maps for complex continued fractions and on a discrete family of generalized Bowen–Series boundary maps. Jointly with Svetla Katok and Ilie Ugarcovici, I have used a variety of tools and techniques to obtain results on geodesic flow on quotients of ${\mathcal H}^2$ by Fuchsian groups. Jointly with Tomasz Downarowicz, I have analyzed subsequences of normal sequences (generic points for shifts) along deterministic sets of indices.