Lecturer, Department of Mathematics, Statistics and Computer Science,
University of Illinois at Chicago
My research lies at the intersection of dynamical systems, topology and geometry. For the past few years, I have been concentrating on the study of topological and algebraic invariants of group and pseudogroup actions on Cantor sets, with the aim of applying them to the classification of laminations and exceptional minimal sets of foliations. A new direction in my recent work is applications of my results in topological dynamics to the study of Cantor actions, arising from representations of Galois groups of fields into the automorphism group of trees. The aim of this work is to find new connections between the topology and dynamics, and arithmetic and number theory.
Upcoming and recent presentations
- Topological methods in dynamics and related topics, Higher School of Economics, Nizhny Novgorod, Russia, January 2019, slides.
- Groupoidfest 2018, University of Illinois at Chicago, November 2018, slides.
- Geometry, Topology and Dynamics Seminar, University of Illinois at Chicago, October 2018, slides.
- Chicago Action Now!, rotating Chicagoland workshop on Dynamical Systems, Group Actions and Geometry, Northwestern University, Evanston, Illinois, May 2018.
Selected recent papers
- O. Lukina, Galois Groups and Cantor actions, arXiv:1809.08475.
- O. Lukina, Arboreal Cantor actions, to appear in Journal of the London Math. Society, arXiv:1801.01440.
- A. Clark, S. Hurder and O. Lukina, Classifying matchbox manifolds, arXiv: 1311.0226, to appear in Geometry and Topology.
- S. Hurder and O. Lukina, Wild solenoids, to appear in Transactions A.M.S., arXiv:1702.03032.
- J. Dyer, S. Hurder and O. Lukina, Molino theory for matchbox manifolds, Pacific J. Math., 289(1) 2017, 91-151, arXiv:1610.03896.