Former Members

Ayreena Bakhtawar's research lies in the intersection of  Diophantine approximation, Fractal geometry and Ergodic theory and dynamical systems. She is particularly interested in exploring the Hausdorff dimension theory of the fractals and the ergodic theory of dynamical systems that comes from various versions of continued fractions. Her research also investigates  the connection between the continued fractions and Diophantine approximation.

[1] Ayreena Bakhtawar, Mumtaz Hussain, Dmitry Kleinbock and Bao-Wei Wang. Metrical properties for the weighted products of multiple partial quotients in continued fractions. Houston Journal of Mathematics, 49(1) (2023), pp.159--194. 

[2] Ayreena Bakhtawar and David Simmons. Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions. Research in Number Theory 9 (2023), no.3, Paper No. 54, 18 pp.

[3] Ayreena Bakhtawar. Hausdorff dimension for the set of points connected with the generalized Jarn'ik--Besicovitch set. Journal of the Australian Mathematical Society, 112(1) (2022), 1--29

[4] Ayreena Bakhtawar, Philip Bos and Mumtaz Hussain. Hausdorff dimension of an exceptional set in the theory of continued fractions. Nonlinearity, 33(6) (2020), 2615--2639

[5] Ayreena Bakhtawar, Philip Bos and Mumtaz Hussain. The sets of Dirichlet non-improvable numbers versus well-approximable numbers. Ergodic Theory and Dynamical Systems, 40(12) (2020), 3217--3235

Michael Levin is interested in topology and topological dynamics. 

[1] Jerzy Dydak, Michael Levin and Jeremy Sieger, Universal spaces for asymptotic dimension via factorization. Canad. Math. Bull.67 (2024), no.2, 391–402.

[2] Michael Levin, Resolving compacta by free p-adic actions. Fund. Math.255 (2021), no.2, 181–207.

[3] Michael Levin, On the unstable intersection conjecture. Geom. Topol. 22 (2018), no. 5, 2511–2532.

Chunlin Liu's primary research focus is on topological dynamical systems and ergodic theory. Additionally, he is studying probability theory, with a particular emphasis on distribution-dependent equations and nonlinear expectations. 

[1] Chunlin Liu, Feng Tan and Jianhua Zhang. Mean Li-Yorke chaos along any infinite sequence for infinite-dimensional random dynamical systems.  J. Differential Equations 403 (2024), 548–575.

[2] Chunlin Liu and Fagner B. Rodrigues.  Metric Mean Dimension via Preimage Structures. J. Stat. Phys. 191 (2024), no. 2, 31.

[3] Jie Li, Chunlin Liu, Siming Tu and Tao Yu. Sequence entropy tuples and mean sensitive tuples. Ergodic Theory Dynam. Systems 44 (2024), no. 1, 184--203.

[4] Chunlin Liu and Leiye Xu. Directional Kronecker algebra for Z^q-actions. Ergodic Theory Dynam. Systems 43 (2023), no. 4, 1324--1350. 

[5] Chunlin Liu and Xiaomin Zhou. Directional entropy dimension of topological dynamical systems. J. Differential Equations 333 (2022), 332--360.

Łukasz Pawelec is working in two directions. One is the dynamics of

entire maps, where he currently studies the behaviour (topological and measure-theoretic) of hairs (and similar objects) for the exponential maps, see [1].

Also, he is interested in ergodic theory, mostly in the recurrence

properties and their applications, e.g. [2].

[1] Łukasz Pawelec, Anna Zdunik, Indecomposable continua in

exponential dynamics - Hausdorff dimension,

Topology and its Applications 178 (2014) 393–410.

[2] Łukasz Pawelec, Mariusz Urbański, Estimating Hausdorff measure for Denjoy maps, Nonlinearity 36 (2023) 6224–6238.