Currently I am studying infinite translation surfaces, in particular I am interested in the ergodic properties of the linear flow on periodic surfaces.

Linear flow on the infinite staircase surface

Publications and preprints

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Ergodic measures for periodic type \(\mathbb{Z}^m\)- skew-products over Interval Exchange Transformations (2023)
Preprint: arXiv

It turns out that even if starting with a uniquely ergodic IET, its skew-products can have many invariant measures. A particularly nice family of invariant measures for infinite skew-products are the Maharam measures, which scale under the Deck group action. Here we show that for the special case of skew-products which are periodic under an extension of Rauzy-Veech induction, the ergodic invariant measures are precisely these Maharam measures. For the proof we use symbolic coding and apply a symbolic result of Aaronson, Nakada, Sarig and Solomyak.

How one can repair non-integrable Kahan discretizations. II. A planar system with invariant curves of degree 6. (With Misha Schmalian and Yuri B. Suris.)
Mathematical Physics, Analysis and Geometry 24, 40 (2021)
arXiv, Journal

This is the outcome of a summer research project done in 2020, supervised by Yuri B. Suris (TU Berlin), together with Misha Schmalian.
We studied the geometry of discrete integrable systems generated by birational maps preserving elliptic curves, and constructed a new one-parameter family of such maps with degree 6 integrals. This family is an example of an integrable discretisation of a continuous integrable system, discretised via Kahan’s method with some higher order term modifications.