Olga Lukina

Assistant Professor

Mathematical Institute

Leiden University

Niels Bohrweg 1

2333 CA Leiden

Email: ollukina940 at gmail.com, o.lukina at math.leidenuniv.nl

My CV

My research lies at the intersection of dynamical systems, topology and geometry, with applications in number theory, percolation and other areas. My recent projects include applications of Cantor dynamics in the study of properties of the profinite Galois groups, and the properties of flows on flat surfaces of infinite genus. I am also interested in group-theoretical and geometric aspects of percolation on Cayley graphs of non-abelian groups.

Research Statement

Events

I am organizing

Probability and Analysis in Leiden and Delft (PALD) seminar, with Kristin Kirchner.
Workshop Dynamics on Zero-Dimensional Spaces: New Connections, Lorentz Center, Leiden, May 13--17 2024, with Maria Isabel Cortez and Samuel Petite.

Upcoming and recent presentations

Workshop `Uniform distribution of sequences', Edwin Schrödinger Institute, Vienna, Austria, April 2025.
General Mathematics Colloquium, Leiden University, December 2024, pdf .
Discrete Mathematics Seminar, Université de Liège, Belgium, November 2024, pdf .
Dynamics Days Europe, minisymposium on Teichmüller Dynamics, Bremen, Germany, July 2024.
Mini-symposium `Integrable Systems and Geometry of Complex Foliations', Université de Bourgogne, France, February 2024.
Workshop `Aperiodic order', Oberwolfach Mathematical Research Institute, Germany, August 2023.

Past lecture series

Barrett Lectures 2022, University of Tennessee at Knoxville, USA, June 2022, first lecture, second lecture.
Ritsumeikan University, Japan, November - December 2019.

Program.
Introduction to group Cantor actions, notes.
Invariants of Cantor group actions, notes.
Cantor actions and Galois groups, pdf.
Stabilizers of points for Cantor group actions.

Selected recent papers

S. Hurder and O. Lukina, Type invariants for solenoidal manifolds, arXiv:2305.00863.
M. I. Cortez and O. Lukina, Settled elements in profinite groups, arXiv:2106.00631, Advances in Mathematics, 404 2022, 108424.
S. Hurder, O. Lukina and W. van Limbeek, Cantor dynamics of renormalizable groups, arXiv: 2002.01565, Groups, Geometry and Dynamics, 15(4) 2021, 1449--1487.
M. Gröger and O. Lukina, Measures and regularity of group Cantor actions, arXiv:1911.00680, Discrete Contin. Dyn. Syst. Ser. A., 41(5) 2021, 2001--2029.
S. Hurder and O. Lukina, Limit group invariants for non-free Cantor actions, arXiv:1904.11072, Ergodic Theory Dynam. Systems, 41(6), 2021, 1751--1794.
O. Lukina, Galois Groups and Cantor actions, arXiv:1809.08475, Trans. Amer. Math. Soc., 374(3) 2021, 1579--1621.

Complete list of publications ...